j    Caiiiornis 


I 


KEY 


TO   THE 


Hebrew-Egyptian  Mystery 


IN 


THE  SOURCE  OF  MEASURES 


ORIGINATING 


THE    BRITISH    INCH    AND   THE    ANCIENT    CUBIT 


BY  WHICH   WAS    BUILT  THE    GREAT  PYRAMID    OF  EGYPT  AND    THE 
TEMPLE    OF    SOLOMON;    AND    THROUGrf  THE    POSSESSION    AND 
USE    OF    WHICH,   MAN,  ASSUMING    TO    REALIZE    THE    CRE- 
ATIVE LAW  OF  THE  DEITY,  SET  IT  FORTH  IN  A  MYS- 
TERY, AMONG  THE  HEBREWS  CALLED  KABBALA 


56  BY 


j;' RALSTON  SKINNER 


PHILADELPHIA : 

DAVID  McKAY  COMPAIW 

WASHINGTON  SQUARE 


6^ 


"  OPEN   THOU    MINE    EYES,  THAT    I   MAY  BEHOLD  WONDROUS    THINGS 

OUT    OF    THY    LAW  ! 

"my    son,    if    THINE     HEART    BE    WISE,    MY    HEART    SHALL    REJOICE, 

EVEN    MINE  : 

"  YEA,    MY    REINS    SHALL    REJOICE,    WHEN     THY    LIPS    SPEAK     RIGHT 

THINGS." 

"behold!    THE    DAY    OF    THE    LORD    COMETH,    AND    IT    SHALL  COME 
TO   PASS    IN    THAT    DAY, 

"  THAT     THE     LIGHT     SHALL     NOT    BE     CLEAR,     NOR    DARK,    BUT     IT 

SHALL    BE    ONE    DAY, 

"and   THE    LORD    SHALL  BE    KING   OVER  ALL    THE    EAJtTH  :    IN  THAT 

DAY    THERE    SHALL    BE 

ONE    J  E  H  O  VA  H , 

AND    HIS    NAME    SHALL    BE 


nS 


N^D^ 


TABLE  OF  CONTENTS. 


Introduction. 


Contents  an  essay  or  study  rather  than,  strictly  speaking,  a  work.  The 
whole  a  series  of  developments  based  upon  the  use  of  geometrical  ele- 
ments, giving  expression  in  numerical  values,  founded  on  integral  values 
of  the  circle,  rediscovered  by  the  late  John  A.  Parker,  and  by  Peter  Metius 
in  the  i6th  century.  Brief  statement  of  these  developments ;  the  greatest 
being  that  the  system  from  whence  their  derivation  was  anciently  consid- 
ered to  be  one  resting  in  nature,  or  God,  as  the  bast's,  or  law,  of  the  ex- 
ertion, practically,  of  creative  design  :  as  such  to  be  found  as  underlaying 
the  Biblical  structure.  This  introduction  contains  the  Hebrew  alphabet, 
with  the  values  and  powers  of  the  letters,  and  some  of  their  supposed 
symbols,  with  some  remarks  on  the  hieroglyphic  use  of  the  letters.  (The 
proof  of  the  uses  of  these  values  by  the  ancients  is  all  that  is  claimed  as 
being  of  use  connected  with  the  quadrature  idea,  so  that  the  usual  ofFen- 
siveness  connected  with  any  stated  idea  of  quadrating  the  circle  is  not  in- 
volved.) 

Quadrature  of  the   Circle  hy  yohn  A.  Parker. 

It  would  be  amply  sufficient  for  the  purposes  of  this  work  to  give  the 
numerical  results  (notating  geometrical  conditions)  of  Mr.  Parker's  quad- 
rature; but  it  is  thought  that  the  uses  shown  to  have  been  anciently  made 
will  naturally  lead  to  a  desire  to  examine  into  the  very  means  whereby 
these  numerical  data  are  obtainable.  To  satisfy  such  a  desire  the  leading 
outlines  of  Mr.  Parker's  work  on  the  quadrature,  and  of  Yn^ problem  of 
three  revolving  bodies,  with  his  uses  of  his  results,  are  given,  even  pretty 
fully,  by  permission.  His  extremely  interesting  work  is  to  be  had  in  the 
city  of  New  York,  of  John  Wiley  &  Son. 

\  I.     Kabbala  a  species  of  symbolic  writing.     Relation   of  diameter  to 

circumference  of  a  circle  a  supreme  one  as  connected  with  the  god-names 

Elohiin  and  Jehovah.    Two  expressions  of  circumference  to  diameter,  in 

(iii) 


IV  TABLE    OF    CONTENTS. 


integrals,  used  in  the  Bible;  that  of  Mr.  Parker,  the  ferfect  one,  and 
that  of  Peter  Metius  (i6th  century),  the  imperfect  one.  One  relation  be- 
tween the  two  expressions  to  be  found  in  §82  (J).').  (§2.  Notice  oi  the 
quadrature  by  Peter  Metius,  about  a.  d.  15S5.)  Outline  of  12  propositions 
from  Mr.  Parker's  Quadrature,  resulting  in  the  key  numbers,  and  values, 
on  which  this  entire  work  depends.  (See  Prop.  XII,  p.  20.)  ^  3.  Quad- 
rature by  Peter  Metius,  with  statement  of  curious  relations  between  the 
Parker  and  Metius  forms. 

Reflections  on  the  Quadrature  by  Mr.  Parker, 

?  4.  ^uadratare  by  Mr.  Parker  of  great  value,  but  set  forth  not  on  ac- 
count of  intrinsic  exactitude,  but  because  :  (i.)  It  affords  the  measures  for 
\i\n\6\n^\ht.  great  pyra7nid ;  (2.)  The  sacred  cudit  was  derived  from  it; 
(3)  ^^  gives  the  kabbalistic  value  for  understanding  the  god-names  in  the 
Bible,  and  for  understanding  the  esoteric  teachings  in  the  mysteries ;  (5.) 
It  appears  at  the  foundation  of  the  British  measures.  Its  great  value  is, 
then,  that  it  is  a  literary  key  to  the  comprehension  of  ancient  learning ; 
and,  in  this  aspect,  its  mathematical  or  geometrical  value  is,  however  im- 
perfect, one  that  is  of  secondary  consideration  in  this  work.  With  this 
statement  it  is  to  be  noted,  §5,  that  Mr.  Parker's  quadrature  values  are 
obtained  by  area  computations;  §6,  that  there  af'e  curious  features  observ- 
able in  the  details  of  the  Playfair  method ;  §8,  that  mathematics  is  famil- 
iar with  definitions  which  are  untrue;  and,  §9,  that  nature  seems  to  afford 
confirmatory  evidence  that  Mr.  Parker  is  right. 

Problem  of  Three  Revolving  Bodies  by  Mr.  Parker. 

?ii.  This  grows  out  of  his  quadrature,  as  a  practical  use  of  his  re- 
sults, for  astronomical  purposes,  his  postulate  being,  "  The  proposition  is 
therefore  demonstrated  that  three  gravitating  bodies  of  equal  magnitude, 
revolving  together,  their  relative  motion  shall  be  as  four  to  three,  or  one 
and  one-third  of  one  primary  circumference."  2  12,  §  13.  Illustration  of 
use  of  this  problem  to  obtain  astronomical  time,  showing  that  nature  rec- 
ognizes the  use  of  the  Parker  numerical  forms.  §  14.  Table  of  astronomi- 
cal time  periods  worked  out  by  Mr.  Parker.  §  15.  The  setting  forth  of 
the  problems  and  claims  of  Mr.  Parker  is  not  in  any  way  as  affirming  the 
establishment  of  the  ''Quadrature,"  or  of  the  '■'Problem  of  three  re- 
volving bodies;"  but  as  necessary,  because,  without  the  use  of  his  con- 
clusions, it  -viiW  forever  prove  impossible  to  reconstruct  the  pyramid  agree- 
ably with  the  intent  of  its  architect. 


TABLE    OF    CONTENTS. 


The  Possibility  on  Mr.  Parker's  Forms  of  Raising  a    Co- 
ordinating Unit  of  Measure. 

\  i6.  This  enunciation  explained,  and  a  numerical  result  given  to  a  geo- 
metrical change  of  shape.  §  17.  This  result  proves  to  be  a  recognized 
measure — viz.,  the  ancient  cubit,  in  terms  of  the  British  foot  and  inch 
measure.  Table  of  practical  restorations  of.  ancient  cubit  value  from  dif- 
ferent sources;  the  best  being  those  of  Sir  Isaac  Newton,  from  the  g-reat 
pyramid,  and  from  the  catacombs  of  Osimandya  bj  the  French  expedi- 
tion of  '99,  the  measures  of  which  catacombs  were  (§  iS)  discovered  on  a 
Turin  papyrus  by  Professor  Gustav  Sejffarth.  §  19.  Original  value, 
whence  this  cubit,  shown  to  have  been  utilized  as  in  British  inches,  creat- 
ing the  impression  that  the  British  long  measures  were  of  that  ancient  ex- 
istence. 

The    Ansated    Cross  of  the    Egyptians.,  and  the   Christian 
/^    Cross.,  the  Embletnatic  Display  of  the   Origin    of  Meas- 
ures. 

?  20.  Circular  measure  taken  off  on  to  the  edges  of  a  cube.  Cube  un- 
folded is  in  display  a  cross  of  the  tau  form,  or  Egyptian  form,  or  of  the 
Christian  cross  form.  Circle  attached  to  the  first,  gives  the  ansated  cross 
of  the  Egyptians.  Numbers  3  and  4  counted  on  the  cross,  showing  a  form 
of  the  golden  candlestick,  and  of  the  3-1-4  =  7,  and  6+1^7,  days  in 
the  circle  of  the  xveek,  as  7  lights  of  the  sun.  (So,  also,  as  the  week  of  7 
lights  gives  origin  to  the  month  and  jca/-,  so  it  is  the  time  marker  of  birth, 
p.  202.)  §21.  The  cross  form  being  shown,  then  by  the  connected  use  of 
the  form  113  :  355,  the  symbol  is  completed  by  the  attachment  of  a  man 
to  the  cross.  This  kind  of  measure  was  made  to  co-ordinate  with  the  idea 
of  the  origin  of  human  life  (?  20),  and  hence  iht  phallic  form.  See  §  23, 
and  comment  by  Professor  Seyffarth  ;  also,  the  symbols  there  displayed. 
§22.  The  vnsin's  head  symbol,  of  the  sphere,  or  circle. 

Primordial    Vestiges  of  these  Symbols. 

§24.  The  Easter  Isles.  Crucified  man  in  South  America.  Hebrew  in- 
scriptions in  the  American  moufids.  Curious  data  regarding  the  mounds 
as  alike  Typhonic  emblems  with  the  pyramid  of  Egypt,  and  with  Hebrew 
symbols.       Mounds    showing     British    measures.      Aztec,    or    "  mound- 


VI  TABLE    OF    CONTENTS. 

builder"  pyramid  showing  the  use  of  the  value  318,  or  diameter  to  a  cir- 
cumference of  one^  as  a  civil  calendar  number.  Old  bronze  axes  of  the 
Phenicians  identical  in  shape  with  the  copper  ones  of  the  mound-builders. 

British  System  of  Long"  and  Land  Afeasure^j^.Jjiclusive  of 
an  Occult  System  of  Time  JlLeasfires. 
§?  25,  26,  27,  and  28,  introductory  to  this  inquiry.  JVofe  to  §  33.  jfe- 
hovah  is  Noah,  in  the  Hebrew,  by  literal  transfer  into  British  is  the  word 
I-nch  (see  also  noie,  page  160.)  :  Also,  «<?/epage  65,  as  to  Jared,  the  father 
of  Enoch,  being  the  Mount  of  Descent.  Jared  literally  is  YRD,  or  the 
British  word  yard,  a  measure;  and  as  source  of  descent  is  the  British  word 
yard,  used  in  the  sense  of  membrum  virile.  (Let  it  be  noted  that  the 
British  part  of  the  language  is,  one  may  say,  almost  purely  Hebrew,  as  is 
fully  within  the  experience  of  students.)  Hebrew  language  noted  for  its 
stem-building.  The  words  fared,  Ararat,  Arets,  earth,  arour,  cursing? 
cognate  forms  under  the  idea  oi  from  a  source,  as  birth,  or  origin.  Sec 
also,  in  this  connection,  Introduction  to  Appendices  (c),  as  to  an  exten- 
sion of  the  same  cognate  form  in  Mars,  as  Generator  o\-  ihc germinating 
principle.  §34.  God-names  Eiohim  and  Jehovah  numerical  indices  of 
geometrical  relations.  God-name  Eiohim,  in  its  radicals,  expressive, 
also,  of  the  differential  yzXn^^  31  and  36.  A  use  shown  of  these  differ- 
entials. \  35.  A  table  showing  a  linking  together  of  values  of  apparently 
incongruous  subjects  matter.  (2.)  Lunar  year  of  ancients  355  —  i  =  354 
days.  Time  scale  of  measures,  year  values,  of  355,  360,  365,  and  354,  359, 
and  364  days.  (3.)  Relation  of  6561  :  20612  to  113  :  355.00014-;  and 
113  :  355-OOOI-I-  to  36  :  113.0973-t-,  where,  by  a  slight  change  113  becomes 
a  circumference  to  a  diameter  of  6  X  6  =  36. 

Introduction  to   Construction  of  Great  Pyramid. 

§  38.  Measures  by  Professor  Piazzi  Smyth,  taken  on  the  British  stand- 
ard at  Edinburgh,  He  found  the  measures  of  Colonel  Howard  Vyse,  of 
the  Tx^r^ch  savants,  and  of  Professor  Greaves,  of  Oxford,  reliable.  \  39. 
(<f.)  Measures  of  passage-ways,  and  chambers,  showing  variations  on 
a  mean  of  measure. 

Standard  Measures  of  the  Pyramid. 

?40.  One  object  of  construction  may  be  taken  as  astronomical,  because 
north  base  side  co\nc\dQS  w\i\\  parallel  of  30°  N.  latitude,  {b.)  Another 
may  be  taken  as  geometrical.  Measures  of  the  mass  by  Professor  Smyth. 
§41.  Standard    measures   shown    in    use    of   Parker   forms.       Compari- 


TABLE    OF    CONTENTS.  vii 


son  with  measures  by  Professor  Sm_yth.   Remarks.  §42.  Standard  measures 
of  the  king's  chamber.    §?43,  44,  45.  Actual  measures  as  enlargements  on 
the  standard,  with  a   reason  for  the  variation,    (i  46.  System    of  enlarge- 
ment applied  to  ascertain  the  measures  of  the  king^s  chamber.     [See  Ad- 
denda,   («.)]      Enlargement  on   the   standard  founded  on   a   law.     (1 47. 
Enunciation  of  this  law.     Note:  Base  side  of  pyramid  diameter  to  a  cir- 
cumference of  2400.     24  is  6  X  4-     Base  of  pyramid  would  then  represent 
co-ordinately  a  square  of  24  to  the  side,  divided  into  4  parts  of  6  each.  This 
is  the  Garden  of  Eden  iorm\  also  that  of  the  Hebrew  Zodiac   (also  that 
of  the  encampment  of  the  Israelites).      §48.  Discovery  of  this   law  de- 
rived from   "Historical  View  of  the   Hindu  Astronomy,"  by  Mr.   John 
Bentley.     Analysis  of  the  Hindu  system,  and  its  object  shown  ;  for  calcu- 
lations  of  sines,   co-sincs,  tangents,    co-tangents,    and   orbits  of    planets. 
Same  object  made  apparent  in  the  measures  of  the  king's  chamber.     §49. 
Note  a  connection  between  the  Parker  and  Metius  forms,  with  relation  to 
the   factor  value  6.     I  50.  Table  of  standard  measures  of  restoration  of 
the  great  pyratnid,   made  thus  far.        §51.  Measures  enlarged  on   the 
standard.     I  52.   Measures  as  actually  made  or  computed   in  terms  of  the 
British  inch  and  foot.     ?  53.  Table  on  these  enlarged  values,  where,  in 
every  case,  31S  is  the  quotient  of  the  diameter  divided  by  the  circumfer- 
ence.    318  Agnostic  value  of  Christ,  and  of  the  trained  servants  of  Abra- 
ham (also  of  the  word  Eliezer  of  Damascus,  Abraham's  steward).     Hindu 
time  periods  founded  on   factor  6.     §54.   System  of  factoring  to  obtain 
the  standard  measures  from  the  Parker  circumference  of  20612. 

Effect  of  Putting  the  Pyramid  in  a   Sphere. 

§55.  To  develop  the  number  216330.  This  number  found  as  an  ellipti- 
cal difference.  True  pyramid  springing  from  a  pyramid  in  the  original 
Parker  numbers  placed  in  a  sphere.  \  56.  Solar  year  value  obtained  fiom 
i  base  side  of  pyramid,  and  the  sine  oi -rp  degrees.  §57.  Equatorial  and 
polar  diameters  of  the  earth  obtained.  Note  (page  104)  :  Length  of  pas- 
sage from  edge  of  great  step,  through  antechamber,  to  king's  chamber, 
taken  from  the  miles  equatorial  value  of  the  earth.  See,  as  to  this,  note, 
page  139.  §60.  Square  root  of  the  solar  year  displayed  in  the  king's 
chamber.  §62.  Hebrew  Biblical  scheme  in  some  measure  bearing  on 
this.  'idZ-  The  base  of  the  pyramid  includes  the  thickness  of  the  pave- 
ment. §^64  and  70.  Location  and  length  of  descending  passage-way, 
with  respect  to  the  inclined  outside,  to  the  base,  and  to  the  vertical  axial 
line  of  the  structure.  §71.  Descending  passage-way  set  off  to  the  east- 
ward of  the  vertical  axial  line  of  the  pyramid,  24.4219-!-  feet.  ?  72.  Di- 
mensions of  the  descending  passage-way.     §  73.  Location  of  intersection 


Vlll  TABLE    OF    CONTENTS. 

of  floor  line  of  ascending  passage-way,  witli  the  roof  line  of  descending 
passage-way.  Floor  line  of  ascending  passage-way,  with  relation  to  the 
base  of  the  pyramid,  to  the  levels  of  the  queen's  and  king's  chamber,  and 
to  the  vertical  axial  line  of  the  mass.  ?  74.  Abstract  geometrical  elements 
laying  at  the  base  of  the  tnlerior  construct iott  of  the  pyramid.  \  75. 
Length  of  king's  chamber  level.  §  76.  Elements  of  dimensions  of  queen's 
chamber.  §  77.  Height  from  floor  of  subterranean  passage-way  to  the 
gable  roof  of  Campbell's  chamber.  ^79.  Height  of  level  of  passage  to 
queen's  chamber  above  the  center  of  the  sphere,  in  which  the  whole  pyr- 
amid is  supposed  to  have  been  placed.  §  80.  A  method  of  placing  a  sa- 
lient height  line  for  the  interior  construction  of  the  pj^ramid.  §  81.  Close 
of  effort  at  reconstruction  of  the  pyramid,  with  remarks.  John  A.  Par- 
ker's method  of  quadrature  and  his  problem  of  three  revolving  bodies 
thought  to  be  the  base  oj  the  Pythagorean  and  Egyptian  systems  of  geom- 
etry and  astronomy.  §  82.  Pyramid  symbolization ;  having  a  Hebraic 
and  Biblical  application  to  set  forth  a  primal  one  under  a  Jehovah  and 
Noah  form.  Jah  is  Noah,  or  Jehovah  is  Noah.,  in  Hebrew  would  be  I^J*, 
or  literally,  in  English,  Inch. 

TJie   Temple  of  Solomon. 

\  84.  Introductory  remarks.  Details  of  description.  Remarks  on  the 
word  cherubim.  Comparison  of  the  measures  of  the  temple  with  those  of 
the  pyramid.  Kabbalistic  elucidations  with  regard  to  astronomical  fea- 
tures of  the  temple. 

Introduction  to  Appendices. 

§85.  (a.)  The  opening  sentence  in  Genesis.  (3.)  Its  parallel  numeri- 
cal reading.  Elohim  a  circumference  value  of  3.1415  to  a  diameter  of  1. 
(c.)  Arets,  earth,  Adam,  man,  and  H-Adam-h,  earth,  are  cognate  with 
each  other,  have  a  like  signification,  and  are  pers07iijicd  under  one  form, 
as  the  Egj'ptian  and  Hebrew  Mars,  (d.)  Enigmatical  constructions  ap- 
pearing in  the  first  face-readings  of  the  Bible  narratives.  Illustrations 
and  examples  given. 

Appendix  I. 

\  86.  The  Garden  of  Eden  an  Adam,  or  144  form.  §87.  The  produc- 
tion of  the  woman  from  the  side  of  the  man,  or  the  number  value  5315 
from  113.  The  rib  a  determinative  ot  the  method,  (c.)  (i.)  The  woman 
form  of  the  garden  the  source  of  the  Holy  of  Holies,  by  type,  and  of  the 
four  typical  rivers.  (2.)  Object  of  the  glyph  to  display  the  Parker  and 
Melius   number  forms  of  20612  :  6561   and  355  :  113.     {<f.)  Other  deter- 


TABLE    OF   CONTENTS.  IX 

minatives.  §  88.  The  Garden  of  Eden  as  the  7th  day.  (The  Hebrew 
words :  sacr,  as  membrum  virile^  the  base  of  the  Latin  sacr  with  facto., 
and  also  of  the  English  5a'cr-ifice  and  5acr-ament;  and  sanctified.,  or  the 
Hebrew  Kodesk,  as  showing  a  sexual  or  productive  use.)  Garden  of  Eden 
display  in  the  Eleusinian  mysteries  by  women,  in  the  use  of  the  basket 
and  serpent.  Curious  learning  as  to  this.  Note:  Mystery  of  the  cross 
but  deepens,  as  one  gathers  knowledge  as  to  it. 

Appendix  II. 

§  89.  Time  calculations  founded  on  Abram,  Mclchizedec,  Hebron.,  or 
Kirjath-Arba,  Joshua  the  son  of  Nun,  and  Caleb  the  son  of  Jephtinneh,  as 
connected  with  the  narratives  relating  to  these  personages.  (Abram  is 
Abra  with  an  appended  m  final,  and  Abra  read  backward  is  Arba,  the  city 
in  which  Abram  lived.)  §  90.  Abraham  and  Isaac  to  be  taken  together  as 
a  year  circle  value  of  355,  which  is  the  Hebrew  word  shanah,  or  year. 
Curious  learning.     Time  year  values  as  355,  360,  365. 

Appendix  III. 

§91.  The  word  Logos,  or  Word,  connecting  with  John,  or  Jonah,  or 
Dove,  with  Jehovah,  and  with  Jes-\x?,,  through  the  fish.  John  the  same 
with  Jonah.  The  word  beginning.  John  and  Jonah  as  Dove.  The 
fish  as  connected  with  Dove,  or  John,  or  Jonah,  to  make  Jehovah,  {f.) 
The  Te  Deum  and  the  birth  of  the  Savior,  (g.)  The  Dove  used  in  cal- 
culations of  the  year.  (^.)  New  Testament  use.  Note,  as  to  the  river 
Jordan  and  its  fisheries. 

Appendix  IV. 

A  method  of  construction  of  the  Julian  Calendar  from  the  different 
year  values  of  the  ancients.  \  92.  Garden  of  Eden  one  of  the  birth  of 
time,  and  of  man.  Year  values,  355,  360,  365 ;  from  these  another  scale 
of  354,  359,  and  364,  of  which  the  last  value,  364,  arises  from  the  -woman 
number 'J,  and  connects  this  as  a  woman  number  with  355,  which  is  an  ab- 
stract circumference  to  a  diameter  of  113,  or  man  value.  Page  229:  Pic- 
tured use  variously  displayed;  Hindu  display  clearly  marking  the  Hebrew 
use;  it  is  that  of  the  woman  hermaphrodite  Indranee-Indra,  the  nature 
goddess,  the  Issa  of  the  Hebrews,  and  the  Isis  of  the  Egyptians.  Page 
2y:): '■'■Remission  of  sins,"  having  reference  to  a  '■'■  neiv  birth  unto  right- 
eousness," explainable  under  the  type  of  shedding  of  blood  in  concep- 
tion. Page  232  :  Julian  Calc7idar  Division.  §  92.  (5.)  The  possible 
heel  meaning  of  the  217  days.     Name  of  Jacob  the  same  as  Jah  is  heel. 


X  TABLE    OF    CONTENTS. 

Page  333 :  Possible  determinative  sentences  in  4th  Genesis.  Seth  same 
as  year.  His  son  Enos.h  same  as  365  —  1  =364,  showing  two  jear  values. 
The  above  use  somewhat  strengthened  by  the  zodiacal  sign  of  the  fishes. 
Page  235  :  The  word  Pdradise  as  having  a  bearing  on  this  subject.  (It  is 
the  same  as  would  be  the  use  of  the  English  expression  Divide-O,  in- 
tended to  mean  the  division  of  a  circle,  the  Hebrew  letter  samech  for  O, 
indicating,  beyond  the  circle,  its  value  of  360°.)  Page  236:  The  Heel 
value  appearing,  as  connected  with  the  measures  of  the  queen's  chamber 
in  the  pj-ramid.  Page  237  :  Curious  learning  as  to  the  meaning  of  the 
ritualistic  fact  of  circumcision.  Relation  of  the  J>repttce  to  the  sacr,  as  of 
the  female  pudenda  to  the  membrum  virile ;  hence  the  type  of  a  spiritual 
marriage  by  consummation. 

Appendix   V. 

The  Flood  and  the  Ark  of  Noah,  ivith  their  Strange  Kabbalistic  Biblical 

Relations. 

§93.  Prefatory  remarks.  Substance  of  the  Old  Testament  lays  in  the 
books  of  the  Lavj.  All  the  rest  but  expansion,  explanation,  targums,  en- 
forcements, etc.  Laiv  divided  into  the  framing  of  the  ritual  and  the 
enunciation  of  the  moral  precepts ;  more  space  taken  up  by  the  former 
than  the  latter.  Building  of  the  pyramid  occupies  the  first  chapters  of 
Genesis.  The  Biblical  containment  of  the  pyramid  structure.  Page  240: 
The  use  of  the  names  Shem,  Ham,  and  Japhet,  as  determinative  of  pyra- 
mid measures,  in  connection  with  the  600-year  period  of  Noah  and  the 
500-year  period  of  Shem,  Ham,  and  Japhet.  Page  241  :  Method  of  calen- 
dar correction  contained  in  the  flood  narrative.  Page  242  :  Correction  of 
the  600-year  period.  The  going  into  the  ark  an  expression  of  the  blotting 
out  of  days  as  a  method  of  calendar  correction.  Page  243 :  The  terms 
"  sons  of  Elohim  "  and  "  daughters  of  H-Adam  "  for  one  thing  astronom- 
ical terms.  Page  243  :  The  1.50  days  of  the  flood  the  correction  of  the 
600-year  period,  and  the  determinative  of  this  use.  The  fixing  a  limit  for 
the  closing  and  opening  of  the  year  at  the  winter  solstice  point,  by  the 
figure  of  the  subsidence  of  the  flood  and  the  grounding  of  the  ark.  Page 
245:  The  word  for  flood,  m'bul;  root-word  bul,  or  name  of  the  rainy 
month.  Page  246:  8th  November  same  as  13th  Julian  style,  by  use  of  the 
epagomenai  days,  making  the  first  40  days  of  the  flood  end  on  the  22d  day 
of  December.  Page  24S :  Curious  learning  as  to  the  balance  of  110  days 
to  make  up  the  150  days.  Other  number  rests  or  stops  in  the  flood  narra- 
tive, involving  the  numbers  113  and  355.  Page  249:  The  number  values 
of  the  birds,  viz.,  113  X  6,  and  355.  Page  250:  Mount  Ararat,  or  Jared, 
or  Yard,  and  its  significations.     The  place  of  Ararat,  or  Mount  Jared,  in 


TABLE    OF    CONTENTS.  XI 

the  Adamic  Chronology.  Page  251:  Astronomical  personification.  Ararat 
same  as  the  Roman  yanus  Bifrons  and  St.  Peter.  Page  252  :  Peter  same 
as  cube  of  5  under  the  name  of  the  stone.  (There  is  a  curious  reflection 
here.  Matthew  16,  v.  18,  says:  "Thou  art  Peter  (rock  or  stone),  and  on 
this  stone  I  will  build  my  church."  The  only  other  place  in  the  gospels 
where  the  word  church  is  used  is  in  chap.  18,  v.  15,6/  seq.,  where  there 
is  commandment  for  the  settlement  of  trespasses  by  the  church.  In 
both  these  places  the  power  of  binding  and  loosing  is  given,  showing  a 
direct  connection.  Contrast  this  with  chap.  5,  v.  23,  et  seq.,  where  there 
is  command  for  reconciliation  with  the  brother  before  bringing  the  gift  to 
the  altar.  Now,  it  is  most  strange  :  the  word  for  church  is  ecclesia,  which 
is  a  term  of  separation,  or  of  the  comers  out  from,  and  could  have  had  no 
existence  until  not  only  after  the  death  of  Jesus,  but  until  the  destruction 
of  the  altar  and  temple  ;  for  so  long  as  there  was  an  altar  and  temple, 
just  so  long  the  Jews,  by  the  commands  of  Jesus,  -were  to  obey  the  law. 
Has  there  been  interpolation  here.'  or  were  these  sentences  used  prophet- 
ically?) Page  253:  Other  types  and  teachings.  Page  254 :  Curious,  but 
illustrative,  opinions  of  the  church  as  to  women.  Page  255  :  The  twofold 
character  of  the  Messiah,  and  its  paralleled  Hebrew  and  Greek  mode  of 
origin.  Page  258 :  The  Meshiac  condition  connected  with  the  geograph- 
ical location  of  the  head-waters  of  the  Jordan  river.  Page  259 :  Curious 
learning  as  to  the  salient  dates  of  Biblical  occurrences  agreeing  with  as- 
tronomical time  marks.  Page  260:  Remark  as  to  the  "  Life  of  Apollonius 
of  Tyana,  by  Philostratus,"  and  its  connection  with  the  life  of  the  Savior. 
Page  261  :  Other  Meshiac  types  and  shadows.  Accounts  for  the  conver- 
sion (which  word  means  turning'  as  on  a  hinge")  of  St.  Paul.  Why  he  was 
Saul  and  Paul.  Page  262  :  Saul  and  David.  (Note  that  while  Saul  was 
son  of  Kish,  in  Hebrew  113,  so  David  was  son  of  Jesse,  or  ^^*, 
and  this  word  placed  in  a  circle  reads  113.)  Page  263  :  Acrostic  uses  in 
the  Bible;  HIS,  and  Shem,  Ham,  and  Japhet.     Roman  badge. 

Appendix   VI. 

§  94.  Grand  determinative  at  the  close  of  the  flood,  going  to  show  that 
the  confusion  of  lip  did  not  necessarily  imply  confusion  of  knoivledgc. 
An  evidence  of  common  p6ssession  of  this  knoxvledge.  §  95.  The  con- 
struction of  the  Tabernacle  as  a  dwelling  of  Jehovah.  Page  271 :  Number 
value  of  name  of  Moses  is  345;  that  of  Jehovah,  in  His  assumed  name  of 
I  am  that  I  am,  is  the  reverse  of  this,  or  543. 


XU  TABLE    OF    CONTENTS. 


Appendix  VII. 

?  96.  An  essay  on  the  fourth  chapter  of  Genesis,  showing  the  continued 
relations  of  the  Garden  of  Eden  measures  as  connected  with  those  of  the 
pyramid,  and  an  attempt  at  deciphering  the  hieroglyphic  or  deeper  read- 
ing of  the  narrative ;  connecting  also  the  plan  of  encampment  of  the  Is- 
raelites (a  Garden  of  Eden  form)  with  the  closing  scenes  of  the  New 
Testament.  (The  idea  is  to  be  noted  here, — in  reference  to  the  fact  found 
in  the  text  that  the  solstice  and  equinox  lines  do  not  divide  the  year  circle 
equally,  and  that  the  half  of  the  year  on  the  autumnal  side  of  the  solstice 
line  is  3  days  larger  than  the  other, — that,  astronomically,  the  three  days 
of  the  Savior  in  the  ark,  ox  ground,  or  grave,  may  have  had  reference  to 
this  fact.  Another  note  is  here  made  as  to  one  of  the  values  of  the  words 
Garden  of  Eden,  shown  in  the  text  to  be  177,  which  may  be  useful.  Ten 
cubits  is  numerically  17.17666+  feet,  and  this  squared  is  the  surface  of 
one  of  the  faces  of  a  cube ;  and  this  multiplied  by  6,  would  equal  the  en- 
tire superficies  of  a  cube.  The  Holy  of  Holies  was  a  cube  of  ten  cubits ; 
therefore,  this  expression  would  apply  to  it.  Now,  the  operation  gives 
17.17662X6  =  1770+;  wherefore,  the  value  of  the  words  Garden  of  Eden, 
as  177,  mzy,for  one  phase,  have  indicated  the  cube  of  the  Holy  of  Holies. 
Further,  as  a  note,  there  seems  to  be  a  connection  between  the  7  (seven) 
fold  of  Cain  and  the  70  (seventy)  fold  of  Lamech,  with  the  7  and  70 
times  of  forgiveness  by  Peter.)  Page  300:  False  rendering  of  the  words 
of  the  Savior  as  given  in  Matthew,  chap.  27,  v.  46.  Page  301  :  This  false 
rendering  a  purposed  one  to  give  force  to  a  mystical  sense.  Page  302  : 
Comments  by  a  clergyman  on  the  "  Study  of  the  Bible,"  appropriate  as 
to  the  contents  of  this  work. 

Conclusion  of  Appendices. 

§  97.  Authorities  for  an  esoteric  reading  of  the  Bible.  Rabbinically. 
By  the  Church.  \  98.  The  esoteric  teaching  confined  to  the  few.  The 
Bible  a  Divine,  or  spiritual  work.  God  -the  immediate  Causer  of  each 
sequence.  He  must  be  a  conscious  entity.  Page  309 :  Mystery,  dark-say- 
ing, and  cloaking,  the  burden  of  the  Testaments.  §  99.  Are  the  keys  of 
this  esoterism  lost.?  Page  309  :  Possessed  by  the  Roman  Catholic  Church, 
and  by  the  Free  Masons ;  and  probably  by  the  Greek  Church  and  the 
Brahmins.  Traces  of  it  in  the  English  Church.  Page  310:  Resolutions  of 
the  Academy  of  Sciences,  and  of  Royal  Society  of  London,  against  en- 
tertaining a  thesis  on  the  subject  of  the  Quadrature,  perhaps  an  indication 
of  a  motive  for  concealment  of  the  hidden  wisdom.     Page  311  :  Two  evi- 


TABLE    OF    CONTENTS.  XUl 

dences  of  the  modern  existence  of  this  knowledge.  Templar  emblem  of 
the  old  man.  (The  five-rayed  star,  or  pentapla,  as  signifying  a  pyramid.) 
The  Genius  of  Free  Masonry,  and  detailed  description  of  its  meaning. 
Page  314:  The  province  oi  ritualism.  Page  315:  Ritualistic  symho\s. 
(a.)  The  T'phillin;  (3.)  '~i\\&  cross  2iX\dL  rosary.  Page  318:  Conclusions 
by  the  author.  A  discovery  by  the  author,  made  as  these  last  sheets  are 
in  the  hands  of  the  printer,  is  too  important  to  be  omitted,  and  must  find 
a  place  here.  It  has  a  bearing  upon  the  whole  work,  both  as  to  Mr. 
Parker's  claims,  as  supporting  them,  and  also  as  to  the  Biblical  contain- 
ment of  his  forms,  as  the  perfect,  or  Divi7ie,  ones.  Mr.  Parker's  work 
goes  to  the  extent  of  showing  an  integral  relation  of  area  of  a  square  to 
that  of  its  inscribed  circle,  and  of  diameter  to  circumference  of  a  circle 
by  use  of  a  basic  nutnber  forin  as  seen.  Now,  if  from  the  same  basic  num- 
ber the  harmony  extends  to  the  development  of  an  integral  relation  be- 
tween the  cube  solid,  and  the  solid  contents  of  its  inclosed  sphere,  this,  by 
harmony,  is  in  very  nature  almost  conclusive  of  the  natural  or  Divine  na- 
ture of  the  origin  of  the  Parker  forms.  Let  the  difference  between  Mr. 
Parker's  relation  of  diameter  of  one  to  circumference,  and  the  accepted 
one  be  first  stated  :  The  accepted  one  is  i  :  3.141592+,  while  that  of  Mr. 
Parker,  being  6561  :  20612,  is  i  :  3.1415942691+.  For  singularity  of  re- 
lations connecting  Biblical  numbers  referred  to  in  the  text  with  geometri- 
cal changes  of  forms,  by  means  of  the  Parker  quadrature  elements,  take 
the  following : 

The  running  values  of  the  letters  of  the  Hebrew  word  man  (J^*{^) 
are  113;  the  full  values,  added,  are  311 ;  and  so,  also,  the  full  value  of  the 
Hebrew  words  the  -woman  (nt^J^^H)'  added,  are  311  :  so  that  311  is  both 
man  and  the  -woman,  while  113  is  man.  The  form  stands  311 — 113,  which 
reads  the  same  either  -way.  But  the  term  man  as  aish  is  a  form  of  Adam, 
a.nd  Adam  is  144;  and  on  the  four  cross  lines  of  the  square,  from  verge  to 
center,  the  values  read,  or  are  taken  as  144 — 441,  or  the  reverse  (and  tak- 
ing the  square  thus  divided  as  the  squared  Zodiac,  while  one  441  is  the 
Hebrew  dami  (441),  or  the  vertical  line  as  the  sun  overhead,  or  solstice 
line  to  the  center  of  the  square,  another  441  is  the  datni  (441),  as  the 
bloods  of  Abel  shed,  and  is  the  line  of  the  ecliptic,  or  equinox,  from  the 
autumnal  edge  to  the  center  of  the  square.)  But  thus  we  have  two  forms — 
viz.,  (i.)  311 — 113,  and  (2.)  441 — 144;  linking  themselves  together.  But 
from  the  matt  form  113,  the  -woman  was  taken  as  5315,  and  there  resulted 
the  form  5315 — 5135;  and  by  dropping  the  two  fives  in  the  center  of  the 
square,  we  had  remaining  the  form  531 — 135,  or  -woman  as  135,  and  its  re- 
verse 531 :  whence  were  derived  the  Melius  and  Parker  forms,  showing 


XIV  TABLE    OF    CONTENTS. 


one  object  of  the  use.  Thus  there  are  three  forms  all  connected  together 
under  the  names  man,  the  -woman,  Adam,  and  -woman,  and  they  can  be 
placed  as — 

3"— 113 
441  —  144 

531—135 
It  is  said  o{  the  -woman  that  she  was  taken  from  Adam,  and  afterward  that 
the  Lord  God  brought  her  to  the  Adam,  showing  some  use  o^  -woman  vfKth. 
Adam  ;  so  take  the  above  form  of  -woman,  or  135,  and  Adam,  or  144,  to- 
gether, 

as  135—144 

or  reversed,  as  531 — 441 ; 

which  last  form,  reversed,  is  Adam  joined  to  woman,  or  the  hermaphro- 
dite iorm.     But  take  it  that  there  is  a  significant  meaning  to  the  form 
531441   {as  t hus  obscured),  as  disclosing  a  development  of  the  Parker 
Quadrature  forms,  thus  : 
Take  the  Parker  forms,  or — 

(i.)  Area  of  square,  6561. 

Of  which  the  side  of  square  is,  81. 

(2.)  Area  of  its  inscribed  circle,  5i53* 

Of  which  the  diameter  is,  81. 

Then  cnanging  area  to  rectification,  or  line,  measure  : 
(3.)  Diameter  being  6561. 

Circumference  is  5153  X  4=  20612. 

And   now  there  develops  from  area  and  line,  to  cubic  measure,  by  a 
wonderful  and  harmonic  sequence,  as  follows  : 
(4.)  The  square  of  Si  to  the  side  in  (i.)  cubed  is 

6561X81=531441 
or  the  connected  form  of -woman  Adam ;  and  now  (as  discovered  by  the 

author  March  10,  1875), 

I  3 

(5.)  The  5£>//</ contents  of  a  sphere  is  to  be  had  by  the  form-;  77  Dia. 

3 
(see    any   geometry);    which   for  a  diameter  of  81    as    in   (i.)   is  81    X 

(3.1415942691 -i-6  =  )  .523699044S+ ;  and,   as  a  i^ct,  this  is  precisely  the 

same  as  20612    [rectification  of  circumference   in   (3-)]Xi35-      So  that 

3 
while  the  area  in  (i.)  changed  into  a  cube  is  81  ,  or  531441,  the  solidity  of 

the  contained  sphere  is  20612  X  i3-5  =  27S262,  showing  a  continued  inte- 
gral relation ;  where  the  solidity  of  the  sphere  is  the  Parker  circumfer- 
ence multiplied  by  135,  or  by  -woman,  and  where  the  solidity  of  the  con- 
taining cube   is  expressed    by   the  reversed   form   of  -woman-Adam,   or 

53M4I- 


TABLE    OF    CONTENTS.  XV 

By  this  a  leading  is  shown  to  closing  up  these  curious  relations,  won- 
derful as  eventuating  in  integrals  : 

(i.)  Relation  of  area  of  square  to  that  of  inscribed  circle. 

(2.)  From  this  is  derived  linear  relation  of  diameter  to  circumference 
of  a  circle. 

(3.)  And,  then,  from  (2.)  the  value  of  linear  circumference  multiplied 
by  ivoman,  or  135,  gives  the  solidity  of  the  sphere  inclosed  in  the  cube  of 
one  of  the  bases  of  which  {1.)  is  the  area;  the  cubic  contents  of  which 

cube  is  Si    or  531441,  or  reversed,  144 — 135,  or  a  use  of  the  joined  values 
of  Adam  and  -woman. 

This  shows  that  there  is /«  nattere  not  only  an  integral  relation  between 
the  value  of  the  area  of  the  circle  inscribed  in  the  square  to  the  area  of 
that  square,  and  between  the  linear  diameter  to  circumference  of  a  circle, 
arising  from  the  same  numerical  forms,  as  stated  by  Mr.  Parker,  but  that 
on  the  same  numerical  basis  it  is  to  be  shown  that  the  integral  relation  of 
the  cube  to  its  contained  sphere  is  531 — 441  to  20612  X  i3-5=  278 — 262  : 
and  this  harmony,  with  such  multitudes  of  others  as  have  been  shown, 
only  goes  to  confii m  the  fact  that  the  Parker  relations  are  the  true  nat/iral 
ones  from  eternity  to  eternit)-  :  and  are  the  ones  on  which  the  Bible  is 
built. 

To  complete  the  integral  relations.     The  surface  of  the  cube  of  81  to 

the  edge  is  one  face  =  6561  X  6;=  39366.     Surface  of  contained  sphere  ^^ 

2 
TT  Dia.    :^3.i4i594269i  X6561  =  20612. 


The  following  and  closing  relation,  discovered  March  17,  1875,  is  too 
important  to  omit,  as  it  has  a  bearing  upon  the  foundations  of  the  quad- 
ra tare. 

Standard  circumference  of  base  of  pyramid  has  been   shown   to  arise 

from  integral  relation  of  diameter  of  6561  to  circumference  of  20612  ;  where 

4^ 
20&12  is  multiplied  by  _„,  and  this  as  inches,  divided  by  12  ^381.7037  + 

feet,  the  half  base  side  of  the  pyramid  ("§  41).  Actual  circumference  of 
base  of  pyramid,  enlarged  on  this,  is  where  the  relation  is  taken  of  cir- 
cumference of  one  to  a  diameter  of  .3183097  +  ,  which  diameter  multiplied 
by  12  =3.8197166+,  and  by  100  =  381.97166+,  gives  a  variation  on  381  •- 
7037  +  -  The  circumference  of  20612  on  which  these  relations  are  raised, 
is  founded  by  Mr.  Parker  on  the  area  of  5153  of  the  circle  inscribed  in  a 
square  of  an  area  of  6561,  the  side  of  which  square  is  81. 


XVI  TABLE    OF    CONTENTS. 

Now,  to  show  that  these  very  elements  of  circular  relation  are  natural, 
and  actually  have  connection  with  the  elements  of  the  square  : 

(i.)  The  mean  proportional  between  381.7037+  and  381.97166-)-  is 
381.S3766+. 

(2.)  The  diagonal  oi  2l  square  whose  side  is  81,  is  114.55129S-I-,  and  this 

divided  by -~  381.83766-r,  or  this  very  mean  proportional  between  these 

circular  elements  :  and  this  shows  that  the  elements  of  the  square  do  of 
themselves  by  nature  contain  relations  to  the  elements  of  the  circle  ;  which, 
again,  proves  that  Mr.  Parker's  results  are  well  taken  according  to  nature, 
and  are  consequently  right. 

The  value  1 145.51298 -h  5  =:  22910+,  is  a  reduction  of  this  connection 
between  circular  and  square  elements,  and  the  author  believes  (from  mem- 
ory)  that  229.10+  is  marked,  in  inches,  as  a  measure  of  antechamber  pas- 
sage in  the  pyramid,  by  Professor  Smyth. 

The  mean  proportional  381.837+  is  the  square  root  of  1458,  or  486  X  3- 

March  22,  1875. 


THE  SOURCE  OF  MEASURES. 


INTRODUCTION. 


The  following,  in  place  of  a  work,  strictly  speaking,  is 
rather  an  essay  or  study.  It  is  like  the  study  of  an  artist, 
where  it  comprehends  many  details  in  outline  going  to 
make  up  a  whoJe,  yet  unfinished  and  subject  to  change, 
here  and  there,  as  the  blending  of  details  may  prove  in- 
harmonious or  incongruous  to  the  general  scope  of  the  de- 
sign. Unlike  such  a  study,  however,  others  can  join  in 
the  labor  of  completing  the  task ;  and  it  is  hoped  that  it 
may  prove  an  incentive  to  that  end. 

The  whole  constitutes  a  series  of  developments,  based 
upon  the  use  of  geometrical  elements,  giving  expression  in 
a  numerical  value.  These  elements  are  found  in  the  work 
of  the  late  John  A.  Parker,  of  the  city  of  New  York,  set- 
ting forth  his  discovery  (but,  in  fact,  the  rediscovery)  of  a 
quadrature  value  of  the  circle.  Upon  this  one,  that  of 
Peter  Metius,  of  the  sixteenth  century,  seems  to  be  a  varia- 
tion. 

Mr.  Parker  makes  use  of  an  element  of  measure  of  the 
equilateral  triangle,  by  which,  as  a  least  unit  of  measure, 
to  express  tha  measure  of  the  elements  of  a  circle  in  terms 
of  the  numerical  value  of  a  square  :  so  that,  as  a  conclu- 
sion, a  square  of  8i  to  the  side,  or  6561  in  area,  shall  con- 
tain a  circle  whose  area  equals  5153;  or,  rectifying  the 
circumference,  a  diameter  of  6561  shall  have  a  circum- 
ference of  5153X4=20612. 


Introduction. 


Let  it  be  understood  that  the  question  of  value  of  the  quadra- 
ture, whether  by  Mr.  Parker,  or  by  Metius,  as  to  whether  it  is 
the  expression  of  exactitude  of  relation,  does  not  arise ;  nor  is  it, 
save  incidentally,  pertinent  to  the  subject-matter  in  hand.  While 
this  work  thus  is  relieved  of  any  necessity  of  examination  into 
the  question  of  the  possibility  of  what  is  called  "  the  quadra- 
ture." or  "■  the  squaring  of  the  circle"  nevertheless,  it  is  neces- 
sary to  a  proper  understanding  of  the  whole  that  some,  to  many 
persons  very  dry,  details  of  Mr.  Parker's  construction  of  his 
quadrature  should  be  set  forth  in  the  very  commencement.  In- 
cidentally, however,  it  is  thought  that  the  matters  established 
herein,  as  having  a  direct  relation  to  the  holy  things  of  God,  as 
laid  down  in  Scripture,  will  force  an  inquiry,  on  the  part  of  de- 
vout people,  into  the  abstract  question  of  "  the  quadrature" 
both  as  received  and  as  set  forth  by  Parker  and  by  Metius  ;  and 
also  into  the  question  of  any  special  value  of  the  quadrature  by 
Parker,  as  related  to  the  generally  accepted  one. 

One  development  is  as  follows  :  The  numerical  value, 
20612,  of  a  circumference  is  made  use  of  to  derive  from  it 
a  unit  of  measure  for  linear,  supe7fcial,  and  solid  meas- 
ure. Thus,  as  a  common  unit  of  measure  is  the  edge  of 
one  of  the  faces  of  a  cube,  and  as  there  are  twelve  edges 
to  the  cube,  the  division  of  20612  by  12- is  the  distribution 
of  this  value  onto  these  12  edges;  so  that  the  quotient, 
which  is  1717. 66+,  is  that  unit  of  measure,  which  is,  how- 
ever it  may  be  used,  convertible  into  circular,  and  again, 
back  into  the  geometrical  elements  whence  derived.  And 
this  is  obtained  by  the  special  numerical  value,  171766-f , 
the  one-twelfth  of  20612,  whether,  as  a  fact,  it  be  used  as  a 
whole  or  as  a  part,  as  1.71766+.  Now,  as  a  fact,  1.71766-f- 
of  the  British  foot  is  the  ancient  cubit  value;  hence,  the 
whole  scheme  thus  far  displayed  has  been  practically  util- 
ized, inasmuch  as  20612  is  thus  seen  to  be  of  the  value  of 
British  inches,  while  its  derivative  of  171 766+,  so  divided 
or  scaled  as  to  represent  i. 71 766+,  is  the  ancient  cubit. 

This  is  confirmed  from  the  fact  of  restoration,  by  means 
of  these  numerical  values,  of  the  great  pyramid  of  Egypt, 
in  terms  of  the  British  measures  thereof  made  of  late  years. 

Another  developnient  is  that,  by  a  variation  on  the  use 
of  these  numerical  values,  taken  systematically,  not  empiri- 


Introduction. 


cally,  a  diameter  value  to  a  circumference  value  of  6  is 
found,  which  is  discovered  to  be  the  basis  of  the  Hindu 
method  for  the  calculation  of  tables  of  sines  and  cosines^ 
tangaits  and  cotangents^  and  of  the  orbits  of  planetary- 
bodies  ;  which  variation,  as  an  enlargement  of  the  above 
values,  on  application,  is  found  to  give  the  exactitude  of 
the  pyramid  measures,  agreeably  to  the  design  of  the  archi- 
tect, thus  again  coupling  a  modern  with  an  ancient  use. 

Another  development  is  that  the  British  system  of  long 
and  land  measures  is  discovered  to  contain  an  occult  or 
obscure  system  of  time  calculations,  based  on  the  fac- 
tor 6,  by  which  it  is  seen  that  the  entirety  of  the  British 
measures  rests  upon  these  anciently  developed  elements, 
and  thus  is,  in  fact,  but  a  phase  of  the  Hindu  system. 
The  factor  6  is  the  base  of  the  acre  and  mile  measure, 
running  up  from  the  inch  and  foot,  and  the  equivalent 
of  the  base  side  of  the  pyramid  (which  is  a  diameter 
value  to  a  circumference  of  24)  is  the  side  of  a  square,  di- 
vided into  four  equal  parts  of  6y^6  each,  in  terms  of  the 
British  foot,  and  necessarily  the  inch  ;  hence  the  advanced 
measures,  as  far  as  the  mile,  are  thus  involved.  But  while 
this  is  so,  the  means  of  obtaining  this  pyramid  measure  is 
through  use  of  the  Parker  elements  ;  hence  the  Parker 
elements  are  thus  connected  with  the  whole  range  of  Brit- 
ish measures. 

But  the  greatest  development  is  that  the  entire  system 
seems  to  have  been  anciently  regarded  as  one  resting  in 
nature,  and  one  which  was  adopted  by  nature,  or  God,  as 
tiie  basis  or  law  of  the  exertion  practically  of  creative 
power — i.  e.,  it  was  the  creative  design,  of  which  creation 
was  practically  the  application.  This  seems  to  be  estab- 
lished by  the  fact  that,  under  the  system  set  forth,  meas- 
ures of  -planetary  times  serve  co-ordinately  as  measures 
of  the  size  of  planets,  and  of  the  peculiarity  of  their  shapes — 
i.  e.,  in  the  extension  of  their  equatorial  and  polar  diame- 
ters, in  terms  of  the  British  measures,  or  the  cubit  meas- 
ures arising,  as  stated,  from  the  forms  of  Mr.  Parker. 

The  true  study  of  the  Deity  by  man  being  in  the  observa- 


Introduction. 


tion  of  His  works,  the  discovery  of  a  fundamental  creative 
law  (in  numbers  and  measures),  as  regards  His  works,  of 
as  wide  and  comprehensive  grasp  as  shown,  would  locate 
the  substance  of  such  a  discovery  as  the  practical  real  tan- 
gible link  between  God  and  man,  as  that  by  which  man 
can  in  a  measure  realize  the  actually  existing  working 
qualities  of  God,  just,  speaking  most  reverentially,  as  he 
would  those  of  a  fellow-man — as,  say,  of  a  mason,  or  of  a 
carpenter ;  thus  revealing  tangible  existence,  likeness,  re- 
lationship, and,  remotely,  companionship.  Such  a  link, 
once  found,  would  constitute  a  base  for  superstructures  of 
recognition,  praise,  worship,  and  copy.  As  a  fact,  this 
system  seems  to  underlie  the  whole  Biblical  structure,  as  a 
foundation  for  its  7'ihialism,  and  for  its  display  of  the  works 
of  the  Deity  in  the  way  of  architecture,  by  use  of  the  sa- 
cred unit  of  measure  in  the  Garden  of  Eden,  the  Ark  of 
Noah,  the  Tabernacle,  and  the  Temple  of  Solomon. 

Such  seem  to  be  the  characteristics  of  development  from 
the  elements  of  quadrature  of  the  late  Mr.  Parker.  The 
extent  to  which  the  development  is  made  so  as  to  compel  a 
mental  assent,  must  be  tested,  of  course,  through  the  con- 
tents of  the  work.  There  is  no  disposition  on  the  part  of 
the  author  to  make  any  assertion  as  to  the  strength  of  his 
work.  What  he  has  done  has  been  done  to  the  best  of  his 
ability,  and  he  believes  that  a  studiously  careful  reading 
of  the  work  done,  will  be  that,  and  alone  that,  upon  which 
any  fair  criticism  can  be  based. 

Since,  after  all,  all  matters  of  science  subordinate  them- 
selves to  any  one  by  which  man  can  arrive  to  a  realizable 
knowledge  of  God,  all  things  in  this  book  are  of  poor  value 
in  every  other  regard,  comparatively,  save  as  they  lead  up 
just  to  this  kind  or  condition  of  knowledge.  Such  being 
the  case,  the  following  statements  may  be  made  as  intro- 
ductory : 

(i.)  The  '•'■^ladrature  of  the  Circle,"  by  John  A.  Par- 
ker, sets  forth  the  integral  relation  of  diameter  to  circum- 
ference of  a  circle  as  6561  to  2061.2,  derived  from  area 
computations,  viz  :  area  of  square  being  6561,  area  of  in- 


Introduction. 


scribed  circle  is  5153  ;  and  diameter  being  6561,  rectifica- 
tion of  circumference  is  5153X4=20612. 

(2.)  It  appears  that  nature  was  regarded  as  making  use 
of  this  numerical  relation,  as  a  law  or  application  of  num- 
bers to  measures,  by  which  to  construct  the  mechanical 
properties  of  the  universe  ;  so  regulating  the  times  of  the 
planets  that  they  should  move  by  a  numerical  system  such 
that  by  it  the  measure  of  their  shapes  was  to  be  obtained  in 
a  definite  class  or  scale  of  measures  adapted  to  the  same 
system  :  so  that  movement  should  co-ordinate  with  size 
under  the  same  system. 

(3.)  However  man  obtained  knowledge  of  the  practical 
measure,  the  British  inch,  by  which  nature  was  thought  to 
adjust  the  planets  in  size  to  harmonize  with  the  notation  of 
their  movements,  it  seems  he  did  obtain  it,  and  esteemed 
its  possession  as  the  means  of  his  realization  of  the  Deity — 
that  is,  he  approached  so  nearly  to  a  conception  of  a  Being 
having  a  mind  like  his  own,  only  infinitely  more  powerful, 
as  to  be  able  to  realize  a  law  0/ creation  established  by  that 
Being,  which  must  have  existed  prior  to  any  creation  (kab- 
balistically  called  the  Word) .  The  knowledge  thus  gained 
was  simply  that  of  the  measure  spoken  of  with  its  uses,  in 
connection  with  the  geometrical  elements  from  whence  it 
sprung. 

(4.)  This  knowledge  as  to  its  origin,  interpretation,  and 
use,  became  somehow  that  of  a  caste  condition.  As  such 
it  was  most  sedulously  concealed,  and  when  set  forth  it  was 
only  in  a  secret  or  very  obscured  way.  One  way  of  set- 
ting it  forth  was  by  hieroglyphic  writing.  This  method  is 
the  burden  of  the  Hebrew  Bible.  Another  way  was  by 
architectural  display.  The  greatest  ever  made  was  in  the 
great  pyramid  of  Egypt ;  the  next  greatest  seems  to  have 
been  in  the  temple  of  Solomon. 

(5.)  It  is  thought  the  restoration  of  this  pyramid  agree- 
ably to  the  design  of  the  architect,  will  affbrd  the  means  of 
translation  of  the  hieroglyphic  meanings  of  the  Hebrew 
Bible,  as,  on  hypothesis,  the  one  was  written  and  the  other 
built  to  set  forth  the  same  natural  problems. 


Introduction. 


The  first  step,  therefore,  necessary  to  the  deciphering 
of  the  hieroglyphic  or  symbolic  meanings  of  the  Hebrew 
Bible,  is  the  restoration  of  the  great  pyramid  after  its  archi- 
tectural conception.  This  is  the  chief  burden  of  this  work  ; 
and  it  is  thouorht  that  the  intent  of  the  architect  has  been 
so  far  recovered  as  to  justify  publication.  Secondarily,  it 
is  to  be  shown  that  the  Temple  was  but  another  architec- 
tural style  of  setting  forth  the  same  measures  with  the  pyr- 
amid. The  balance  of  the  matters,  condensed  as  much  as 
possible  into  brief  outline,  chiefly  serves  to  exemplify  the 
method  of  Biblical  application  of  the  pyramid  system. 
This  balance  is  noted  here  and  there  in  the  text,  and  is 
contained  in  the  appendices.  It  serves  to  relieve  the  dry 
details  of  figures  and  calculations,  to  show  related  connec- 
tions, and  is  hoped  to  excite  interest  in  the  whole  subject, 
and  to  stimulate  those  who  may  read,  to  an  earnest  effort 
in  the  further  prosecution  of  this  subject  so  fascinating  in 
its  elucidations. 


The  relation  of  6561  :  20612  is  both  in  the  pyramid 
structure  and  in  the  Bible  coupled  with  the  form  113  :  355. 
Some  connections  between  the  two  will  be  shown,  but  what 
the  exact  basic  relations  between  them  were,  as  anciently 
recognized,  remains  to  be  discovered. 


The  Hebrew  Alphabet. 


THE  HEBREW  ALPHABET. 

For  the  general  reader  to  understand  how  a  numerical 
or  mathematical  system  may  lie  closed  up  in  the  Hebrew 
Bible,  it  may  be  well  to  state  that  the  Hebrews,  so  far  as 
has  come  down  to  us,  had  no  numeral  system,  apart  from 
their, literal  one — i.  e.,  their  alphabet  held  their  numerals, 
just  as  if,  in  English,  our  a,  b,  c,  stood  for  i,  2,  3,  and  so 
on,  in  lack  of  the  Arabic  system  of  numerals,  borrowed  by 
us,  and  now  of  exclusive  use  (although  it  would  seem 
that  they  were  in  possession  of  this  system  also).  The 
following  is  a  table  for  reference,  giving  the  Hebrew  al- 
phabet, the  power  of  the  letters,  their  symbols  to  some  ex- 
tent, with  the  numerical  value  fixed  to  each  letter.  The 
laws  of  svmbolic  use  of  words  as  numbers  in  the  narrative 
of  the  Bible  are  not  known,  and  the  real  uses  are  only  to 
be  accepted  or  received  to  the  extent  for  which  there  is  in- 
trinsic proof.  Otherwise,  it  is  to  be  observed  that  where 
the  letter  values  rise  above  units  to  tens  and  to  hundreds, 
while  the  letter  character  may  stand  for,  say,  20  or  200, 
very  frequentlv  the  characteristic  value  is  used  as  giving 
the  expression  of  the  unit  value  2  alone.  Thus,  the  letters 
yy^,  or  the  signs  of  2,  20,  and  200,  may  be  read  by  their 
characteristics  of  2,  2,  2,  without  special  reference  to  the 
ciphers.  So,  also,  ^^  may  be  read  as  123,  whereas,  by 
adding  as  the  values  are  indicated,  the  sum  would  be  510. 
In  many  instances,  too,  the  right  numbers,  found  by  one 
expression,  are  also  made  use  of,  by  a  reverse  reading,  for 
some  other  use,  connected  or  not.  Again,  the  use  may  be 
of  numbers,  simply  placed  above  the  letters  of  a  word, 
read  perhaps  in  the  reverse,  or  of  the  sum  of  the  full 
values,  addition  being  made.  Thus,  the  above  number 
maybe  used  as  123  or  321,  or  510  or  015,  agreeably  to  the 
indications  to  be  gathered  from  the  context  and  the  con- 
nections, or  from  determinatives  of  the  proper  or  intended 
use  to  be  found  in  the  text. 

A  very  remarkable  feature  of  Hebrew  usage  is  in  the 


8  Introduction. 


permissible  interchange  of  letters  of  like  class,  and 
sometimes  of  unlike  classes — thus,  the  letters  of  any  one 
class,  as  gutturals^  etc.,  are  interchangeable,  and  may  be 
made  use  of  sometimes  without  change  of  the  meaning  of 
the  word,  frequently  for  the  purpose  of  working  out  a 
slight  modification  of  meaning,  sometimes  to  indicate  a 
very  marked  departure  of  meaning.  A  good  and  very  im- 
portant illustration  of  this  may  be  given.  The  verbal  ^^1, 
or  Hay  ah,  or  E-y-e,  means  to  be,  to  exist,  while  11^11,  or 
Chayah,  or  H-y-e,  means  to  live  as  motion  of  existence. 
The  letter  *,  or  /,  ory',  ox  y,  in  these  words,  is  interchange- 
able with  the  letter  •),  or  vau,  or  w,  and  the  two  words  may 
be  read  as  TWT\  or  mn,  without  change  of  meaning.  The 
first  becomes  Havah,  or  Eve,  and  the  second  becomes 
Chavah,  or  Ch-v-e,  and  their  meanings,  as  above,  being 
so  slightly  modifications  of  each  other,  they  are  as  words 
interchangeable  one  for  the  other — that  is,  one  may  be  taken 
for  the  other.  Now,  the  first,  literally,  is  Eve,  while,  as  a 
substantive,  the  second  means  mother,  and  is,  in  fact,  the 
proper  name  as  given  in  Genesis  for  Eve,  the  mother  of  all 
living.  The  Deity  name,  J'hovah,  is  a  compound  of  two 
words,  viz.,  %  or  yah,  and  hovah,  or  IT)!!,  one  of  the  very 
words  in  question.  The  word  Jehovah,  or  fah-Eve,  has 
the  primary  significance  of  hermaphrodite  existence  or 
being,  as  male-female,  and  is  mH"^,  of  which  the  »,  or  /, 
or  y,  or  y,  stands  for  yah,  or  male,  while  T\*ST\  is  a  change 
upon  the  word  mil,  for  the  purpose  of  getting  the  nu- 
ineral  form  of  565  for  865  (originating  in  the  yoni  word 
fsh,  or  pj=565)  :  niH  as  the  woman,  or  Eve,  making 
up  the  male-female  word  Jah-Eve,  was  the  primary  intent, 
the  less  significant  word  mil,  as  of  i7iere  being,  taking 
the  place  of  the  more  significant  one,  for  the  sake  of  the 
number  value  (springing  through  H^,  or  565,  as  a  flux), 
which,  in  another  view,  as  will  be  seen,  is  of  the  utmost, 
and  really  of  paramount  importance.  Thus,  while  it  may 
be  said  that  none  but  a  very  slight  change  has  been  made 
in  the  word  forms,  as  to  their  meanings,  a  very  marked 
change  has  been  made  numerically,  which  was  the  pur- 


The  Hebrew  Alphabet. 


pose  of  the  change.  The  great  power  of  kabbala  rests 
upon  this  kind  of  play,  and  is  thus  derived.  Ordinarily, 
grammatically,  however,  the  same  is  worked  under  a  law 
of  construction.  Under  the  title  "  Orthographic  Changes," 
in  his  Hebrew  Grammar,  Green  says  : 

"  The  signs  (of  the  alphabet)  thus  far  described  represent  all 
the  sounds  of  the  Hebrew  language.  Its  stock  of  words  is  formed 
by  combining  these  in  various  significant  ways.  The  laws  of  such 
combinations,  and  especially  the  mutations  to  which  they  are  sub- 
ject, or  which  they  occasion,  next  demand  attention.  When  a 
particular  idea  has  been  attached  to  a  certain  combination  of 
sounds,  its  different  modifications  may  naturally  be  expressed  by 
slightly  varying  those  sounds.     This  may  take  place — 

"  I.  By  the  substitution  of  one  letter  for  another  of  like  charac- 
ter, and  for  the  most  part  of  the  same  organ,  e.  g. : 
TX'T\  to  be^  to  exist ;  n*n  ^^  I  I've. 

"  2.  By  transposition  of  letters,  e.  g. : 

VIS  to  deal  violently ;  ^^^i3  to  urge. 

"  3.  By  the  addition  of  a  letter. 

>1<**  *>!<>(;  5[<;i<^ 

"  Such  literal  changes  as  those  just  recited  not  only  serve  to  ex- 
press new  shades  of  meaning,  but  even  where  the  meaning  re- 
mains precisely  the  same,  they  may  represent  diversities  of  other 
sorts.  *  *  *  The  lexicographer  regards  such  words  (under- 
going such  changes)  as  cognate,  and  traces  them  back  to  their 
common  source." 

These  subjects  can  be  but  touched  on  in  this  work.  Vol- 
umes have  been  written  on  them,  and  it  would  be  well  to 
treat  them  more  at  large  in  this  connection  could  it  be  done 
in  a  manner  not  to  confuse  the  main  object.  It  must  suf- 
fice to  close  with  the  Alphabet  table. 

No.  Form  and  power.  Name.  Symbol. 

1.  J^     a      scarcely       audible  Aleph.       Ox  or  Bull. 

breathing. 

2.  ^     <5,  (5//,  or  bv.  Beth,         House. 

3-     .3     S^^^^-  Gi'mel.      Camel,  serpent  erect 

(Sharpe). 
4.     "J     c/,  dh.  Da'leth.     Door,  07pQ<:}a[u(;diingc? 


lO 


Introduction. 


No. 


Form  and  power. 


5- 

n 

,^;  Latin  e;   Greek  ^ ; 
smooth      breathing 
(Fuerst). 

6. 

1 

V  or  iv. 

7- 

r 

z. 

8. 

n 

ch^  kh,  hh;  Latin  h; 

Greek  H,  v;  rough 
breathing,  or  the 
Greek  x  (^Fuerst). 


Name. 

He. 


Van. 

Zayin. 

Cheth. 


Symbol. 

Window  opening, 
womb  (Kabbala), 
also  part  of  the 
fence  of  the  letter 
n  (Fuerst). 

Nail,  hook,  (crook, 
Egyptian?). 

Weapon,  (Scepter, 
Egyptian  ?). 

Fence,  ^Hi  Venus 
(Seyffarth).  Affin- 
ity with  n?  as  the 
womb. 


JVote,  that  the  letters  |7  and  |7  are  from  the  same  source,  and 
are  taken  as  the  divided  halves  of  one  oblong  (of  two  squares), 
with  a  little  opening  in  one  end  as  seen  in  H-  The  letter  H  is  5, 
or  a  cube  of  five,  while  H  is  8,  showing  the  number  of  cubes 
taken  to  make  a  larger  one.  (So  8  thus  used,  is  the  same  as  5 
duplicated,  for  5''=i25,  and  125X8=1000,  and  a  larger  cube 
made  from  the  smaller  of  five,  will  make  5+5,  or  10  to  the 
side.) 


9-     D     t. 


10. 


y 


,  2,  or 


J' 


Teth.  Snake,  basket,  figur- 
ed  in  Eleusinian 
mysteries  in  wor- 
ship by  women 
(Sharpe's  Egypt). 
Perhaps  the  scro- 
tum,(Inman).  Love 
apples  (plural  of 
word  for  David^ 
meaning  also  bas- 
ket?) 

Yodh.  Hand,  bent  forefin- 
ger, mcmbrum  vi- 
rile with  testes 
(Kabbala).  The 
perfect  number,  or 
one  (Kabbala). 


The  Hebrew  Alphabet.  ii 


No.  Form  and  power  Name.  Symbol. 

20.     D  "1   c,  c//,  /f',  kh.  Caph.  The    hollow   of    the 

bent  hand ;  with 
^  =  ^^  =  cube^ 
measure  of  hollow 
sphere    (Kabbala). 

30.     7        /.  Lil'medh.      Ox-goad;    sign  of  a 

form  of  the  god 
Mars. 

40.     D  D  ^'  Mem.  Water. 

50.     ^    \    n.  Nun.  Fish,  symbol  of  To- 

ni,  O,  woman,  or 
■womb  (Kabbala). 

60.     ^       s.  Sa'mech.       A  prop,  a  pillar ;  tes- 

tis (  S  h  a  r  p  e  )  , 
hence,  egg.  Di- 
visions of  the  cir- 
cle, perhaps  indi- 
cating a  square. 
Divisions  of  Para- 
dise (Kabbala). 

70.     ^       no  power.  Ayin.  Eye. 

80.     £3  v1  p,ph.  Pe.  Mouth. 

90.     ^^'  Y  ts,  tz.  Tsa'-dhe.      Fish-hook,     hunter's 

dart. 
100.     p       i.  Koph.  Back   of  head   from 

the  ears ;  hence, 
significant  of  bal- 
ances. Ancient  pil- 
low to  rest  the  back 
of  head  on.  Scull.? 
Eye  of  needle. 
200.     "n       r.  Resh.  Head,  sphere,  circle. 

300.     ^      sA,  s.  Shin,  Sin.   Tooth. 

400.     fi       t,tJk.^  Tau.  Cross,    +.     Founda- 

tion framework  of 
construction. 


12  Parker's  Quadrature  of  the  Circle.        §  i, 


CHAPTER  I. 

SECTION  I. 

QJJADRATURE    OF   THE    CIRCLE. 

By  JOHN  A.  PARKER. 


(§  I.)  Kabbala  was  a  species  of  symbolic  writing  among 
the  initiated,  setting  forth  the  secret  teachings  of  the  Bible  ; 
and  the  key  of  Kabbala  is  thought  to  be  the  geometrical 
relation  of  the  area  of  the  circle  inscribed  in  the  square,  or 
of  the  cube  to  the  sphere,  giving  rise  to  the  relation  of  di- 
ameter to  circumference  of  a  circle,  with  the  numerical 
value  of  this  relation  expressed  in  integrals.  The  relation 
of  diameter  to  circumference  being  a  supreme  one  con- 
nected with  the  god-names  Elohim  and  Jehovah  (which 
terms  are  expressions  numerically  of  these  relations,  re- 
spectively— the  first  being  of  circumference,  the  latter  of 
diameter),  embraces  all  other  subordinations  under  it.  Two 
expressions  of  circumference  to  diameter  in  integrals  are 
used  in  the  Bible  :  (i.)  The  perfect ;  and,  (2.)  The  imper- 
fect. One  of  the  relations  between  these  is  such  that  (2)  sub- 
tracted from  (r)  will  leave  a  unit  of  a  diameter  value  in 
terms,  or  in  the  denomination,  of  the  circumference  value 
of  the  perfect  circle,  or  a  unit  straight  line  having  a  perfect 
circular  value,  or  a  factor  of  circular  value  (§  82). 

Of  course,  as  to  the  fact  of  these  expressions  residing  in 
the  Bible,  it  remains  to  be  seen  whether  this  is,  or  is  not, 
so.  It  will  be  sufficiently  strange  if  it  is  so  ;  but  if  it  shall 
so  appear,  beyond  contradiction,  it  will  afford  much  food 
for  thought,  as  to  whether  so  sublime  a  work  as  the  Holy 
Record  can  be  a  refuge  for  that  so  much  oppressed  and 


§  2.        Parker's  Quadrature  of  the  Circle.  13 

bedeviled  idea  of  "  squaring  the  circle^''  unless  the  actual- 
ity of  such  relation  exists,  or  unless  an  approximate  of  a 
certain  nature  and  value  was  found  to  be  of  some  natural 
use. 

(§  2.)  It  is  very  remarkable  :  One  of  the  values  thus 
used  in  the  Bible  was  rediscovered  in  about  A.  d.  1585,  by 
Peter  Metius,  as  113  for  diameter  to  355  for  circumference, 
which,  in  the  Sacred  Record,  is  the  imperfect  value ;  the 
other  was  rediscovered  by  the  late  John  A.  Parker,  of  the 
city  of  New  York,  as  6561  for  diameter  to  20612  for  cir- 
cumference, which,  in  the  Sacred  Record,  is  the  perfect 
value.  What  the  means  of  discovery  by  Metius  were,  is 
not  known.  The  '■'■  ^ladrature'"  of  Mr.  Parker  is  in 
print,  and  therein  the  steps  are  fully  set  forth.  As  to  these, 
as  they  contain  the  geometrical  key  for  the  proper  under- 
standing of  Kabbala,  it  is  necessary  to  set  them  forth  some- 
what at  large,  premising  that  his  value  is  obtained  through 
the  value  of  areas  of  shades.  His  leading  propositions 
(each  proposition  in  the  text  being  followed  by  its  demon- 
stration) are  as  follows  : 

'■'■Proposition  I. 

"  One  of  the  relative  properties  between  straight  lines 
and  a  perfect  curve  or  circle  is  such,  that  all  regular  shapes 
formed  of  straight  lines  and  equal  sides,  have  their  areas 
equal  to  half  the  circumference  multiplied  by  the  least  ra- 
dius which  the  shape  contains  (which  is  always  the  radius 
of  an  inscribed  circle),  than  which  every  other  radius  con- 
tained in  the  shape  is  greater,  and  the  circle  has  its  area 
equal  to  half  the  circumference  multiplied  by  the  radius,  to 
which  every  other  radius  contained  in  the  circle  is  equal. 

^'•Proposition  II. 

"The  circumference  of  any  circle  being  given,  if  that 
circumference  be  brought  into  the  form  of  a  square,  the 
area  of  that  square  is  equal  to  the  area  of  another  circle, 
the  circumscribed  square  of  which  is  equal  in  area  to  the 
area  of  the  circle  whose  circumference  is  first  given. 


14  Parkers  Quadrature  of  the  Circle.        §  2. 

*■'•  Proposition  III. 

"  The  circle  is  the  natural  basis  or  beginning  of  all  area, 
and  the  square  being  made  so  in  mathematical  science,  is 
artificial  and  arbitrary. 

'"'•Proposition  IV. 

"  The  circumference  of  any  circle  being  given,  if  that 
circumference  be  brought  into  any  other  shape  formed  of 
straight  lines  and  of  equal  sides  and  angles,  the  area  of 
that  shape  is  equal  to  the  area  of  another  circle,  which  cir- 
cle being  circumscribed  by  another  and  similar  shape,  the 
area  of  such  shape  circumscribing  the  last-named  circle  is 
equal  to  the  area  of  the  circle  whose  circumference  is  given. 

*'■  Proposition    V. 

*'  The  circumference  of  a  circle  by  the  measure  of  which 
the  circle  and  the  square  are  made  equal,  and  by  which 
the  properties  of  straight  lines  and  curved  lines  are  made 
equal,  is  a  line  outside  of  the  circle  wholly  circumscribing 
it,  and  thoroughly  inclosing  the  whole  area  of  the  circle, 
and  hence,  whether  it  shall  have  breadth  or  not,  forms  no 
part  of  the  circle. 

'■'■Proposition    VI. 

"  The  circumference  of  a  circle,  such  that  its  half  being 
multiplied  by  radius,  to  which  all  other  radii  are  equal,  shall 
express  the  whole  area  of  the  circle,  by  the  properties  of 
straight  lines,  is  greater  in  value  in  the  sixth  decimal  place 
of  figures  than  the  same  circumference  in  any  polygon  ot 
6144  sides,  and  greater  also  than  the  approximation  of 
geometers  at  the  same  decimal  place  in  any  line  of  fig- 
ures." 

Under  this  proposition  after  his  demonstration,  he  states  : 
"And  it  is  evident  that  if  a  circle,  and  a  polygon  of  6144 
sides  (the  number  to  which  Playfair  carries  his  bisection) , 
shall  have  the  same  circumference,  the  area  of  the  circle 
is  greater  than  the  area  of  the  polygon  in  the  sixth  decimal 
place ;  and  because  the  circumference  of  one  diameter  must 


§  2.       Parker's  Q^jadrature  of  the  Circle.  15 

be  four  times  the  area  of  the  circle,  therefore,  by  the  tran- 
sition of  shape  to  a  circle,  the  true  value  of  circumference 
is  greater  in  the  sixth  decimal  place  than  any  approxima- 
tion which  can  be  obtained  from  a  polygon  of  6144  sides, 
whether  inscribed  or  circumscribed." 

'"'■  Proposition    VII. 

"  Because  the  circle  is  the  primary  shape  in  nature,  and 
hence  the  basis  of  area ;  and  because  the  circle  is  meas- 
ured by,  and  is  equal  to  the  square  only  in  ratio  of  half  its 
circumference  by  the  radius,  therefore,  circumference  and 
radius,  and  not  the  square  of  diameter,  are  the  only  na- 
tural and  legitimate  elements  of  area,  by  which  all  regular 
shapes  are  made  equal  to  the  square,  and  equal  to  the  cir- 
cle. 

^'Proposition    VIII 

*'  The  equilateral  triangle  is  the  primary  of  all  shapes 
in  nature  formed  of  straight  lines,  and  of  equal  sides  and 
angles,  and  it  has  the  least  radius,  the  least  area,  and  the 
greatest  circumference  of  any  possible  shape  of  equal 
sides  and  angles. 

'•'•Proposition  IX. 

"  The  circle  and  the  equilateral  triangle  are  opposite  to 
one  another  in  all  the  elements  of  their  construction,  and 
hence  the  fractional  diameter  of  one  circle,  which  is  equal 
to  the  diameter  of  one  square,  is  in  the  opposite  duplicate 
ratio  to  the  diameter  of  an  equilateral  triangle  whose  area 
is  one. 

"  By  diameter  of  the  triangle,  the  perpendicular  is  here 
meant,  as  explained  in  the  introduction  to  Chapter  I.,  or 
a  line  passing  through  the  center  of  the  triangle,  and  per- 
pendicular to  either  side. 

"  Let  it  be  supposed  that  the  areas  of  the  equilateral  tri- 
angle A  and  the  square  C  each  equals  one. 

"  It  has  been  shown  (Proposition  VIII),  that  the  triangle 
has  the  least  number  of  sides  of  any  possible  shape  in  nature 
formed  of  straight  lines ;  and  the  circle  is  the  ultimatum 
of  nature  in  extension  of  the  number  of  sides.    In  this  par- 


1 6  Parker's  Qijadrature  of  the  Circle.        §  2. 


ticular,  therefore,  they  are  opposite  to  one  another  in  the  ele- 
ments of  their  construction.  By  Proposition  VII  it  is 
shown  that  circumference  and  radius  are  the  only  natural 
and  legitimate  elements  of  area  by  which  different  shapes 
may  be  measured  alike,  and  are  made  equal  to  one  another. 
By  Proposition  VIII,  it  is  shown  that  the  triangle  has  the 
least  radius  of  any  shape  formed  of  straight  lines  of  equal 
sides  and  of  the  same  circumference,  and  by  Propositions 
II  and  IV,  Chapter  I,  it  is  seen  that  the  circle  has  the 
greatest  radius  of  any  possible  shape  of  the  same  circum- 
ference. By  the  same  propositions,  the  triangle  is  shown 
to  have  \}i\Q  greatest  circumference  and  the  least  area  of  any 
shape  formed  of  straight  lines  and  equal  sides,  and  the 
circle  is  shown  to  have  the  least  circumference  and  the 
greatest  area  of  any  shape.  By  a  well-known  law  of 
numbers  and  geometry  by  which  the  greatest  product 
which  any  number  or  any  line  can  give,  is,  to  multiply  half 
by  half,  it  will  be  seen  that  if  we  take  the  aggregate  of 
circumference  and  radius  in  each  shape,  it  is  most  equally 
divided  in  the  circle,  and  the  most  U7ieqiially  divided  in  the 
triangle  of  any  possible  shape.  In  every  case,  that  which 
is  ^r(?«/c5/ in  the  triangle  is  least  in  the  circle,  and  that 
which  is  least  in  the  triangle  is  greatest  in  the  circle  ;  and 
in  every  particular  the  two  shapes  are  at  the  extreme  and 
opposite  boundaries  of  nature^  being  the  greatest  and  the 
/t'a5/that  is  possible.  They  are,  therefore,  opposite  to  one 
another  in  all  the  elements   of  their  construction.     There- 


§  2.        Parker's  Quadrature  of  the  Circle. 


17 


fore,  the  square  being  made  the  artificial  basis  of  area 
(Proposition  VIJ),  if  the  diameter  of  the  circle  B  (Plate 
XVI)  shall  equal  the  diameter  of  the  square  C,  tlien,  in 
the  fractional  relations  of  B  to  C  such  diameter  shall  be  in 
the  opposite  duplicate  ratio  to  the  diameter  of  A  corre- 
spondingly situated.  The  diameter  of  A  correspondingly 
situated  with  the  diameter  of  B  to  C,  it  will  be  seen,  is  a 
line  drawn  across  the  center  of  A  perpendicular  to  either 
side;  therefore,  the  diameter  of  B,  in  its  fractional  relation 
to  C,  is  the  opposite  duplicate  ratio  to  the  -perpendicular 
or  diameter  of  A,  and  no  otiier  result  is  possible  in  the  na- 
ture of  things.  (See  Proposition  VII,  Appendix,  and  re- 
marks following.)  The  proposition  is  therefore  demon- 
strated. 

'■''Proposition  X. 

"  The  fractional  diameter  of  one  circle  which  is  equal  to 
the  diameter  of  one  square,  being  in  the  opposite  ratio  to 
the  diameter  of  the  equilateral  triangle  whose  area  is  one, 
equals  81. 


"Let  the  area  of  the  equilateral  triangle  A  (Plate 
XVII)  —I,  and  let  the  area  of  the  square  B  also  equal  one, 
then  the  diameter  of  the  circle  C,  which  is  equal  to  the 
diameter  of  the  square  B,  also  equals  one.  And  it  has 
been  demonstrated  that  in  their  fractional  relations  to  the 
square,  the  diameters  of  A  and  C  are  in  opposite  ratio  to 
one  another.  (By  the  diameter  in  the  triangle  it  is  known 
that  the  perpendicular  is  here  meant,  as  in  Proposition  IX.) 


1 8  Parker's   Quadrature  of  the  Circle.        §  2. 

Now,  if  the  area  of  the  equilateral  triangle  A  shall  equal 
one,  then  the  diameter  of  A  is  found  to  be  equal  to  the 
square  root  of  three  twice  extracted,  or  J  J3.  Hence  the 
fractional  diameter  of  C,  being  in  the  opposite  duplicate 
ratio  (which  is  the  squares  of  diameter),  shall  equal  3 
twice  squared,  or  3'X3^  and  3X3=9,  and  9X9=81.  The 
proposition  is  therefore  demonstrated." 

The  opposite  duplicate  ratio  of  Mr.  Parker  has  relation 
to  the  numerical  values.  The  shapes  being  opposite  to 
each  other,  he  desires  to  get  an  integral  number  to  co- 
ordinate with  the  shapes.  When  the  area  of  A=i,  then 
the  diameter  is  found  to  be  1.316074-I-.  But  this  will  not 
do,  for,  if  possible,  it  must  assume  the  form  of  a  least  in- 
tegral number.  Square  this  value,  and  it  equals  i  .7320508+- 
This  will  not  do.  Square  it  again,  however,  and  it  equals 
3,  which  is  just  that  to  be  desired.  Having,  however,  ob- 
tained this,  the  value  in  the  opposite  ratio  must  suffer  the 
same  process,  and  3"=9,  and  9"=8i. 

'"'•Proposition  XI. 

"The  fractional  area  of  one  square,  which  is  equal  to 
the  area  of  one  circle,  equals  6561  ;  and  the  area  of  the 
circle  inscribed  in  one  square  equals  5153-" 

"  It  has  been  proved  (Proposition  X)  that  the  fractional 
diameter  of  the  circle  C,  which  is  equal  to  the  diameter  of 
one  square  (B),  whose  area  is  one,  being  in  the  opposite 
ratio  Xo  a  b  (Fig.  A),  equals  81  ;  hence  the  area  of  B= 
81X81=6561  ;  therefore,  B  equals  one  of  6561  equal  frac- 
tional parts.  Now,  let  B  equal  H  in  area.  It  has  been 
proved  (Proposition  II)  that  H  equals  E  in  area  ;  and  if 
H=i,  then  E=i  ;  and  if  H=656i,  then  E=656i.  It  lias 
also  been  proved  (Proposition  II)  that  if  the  circumference 
of  F  equals  the  circumference  of  E,  then  F  and  G  are  also 
equal  in  area.  And  because  one  circle,  which  is  equal  to 
one  square  (the  area  of  the  square  being  one),  is  in  6561 
equal  fractional  parts,  therefore,  any  circle  which  is  equal 
to  any  square  (the  diameter  of  the  circle  being  a  whole 
number)  shall  be  in  some  definite  and  certain  number  of 


§  2.        Parker's  Quadrature  of  the  Circle. 


6561  parts.     Hence,  the  areas  of  the    circles    C    and    G 
(their  diameters  being  each  81)  are  some  definite  and  cer- 


tain number  of  6561  parts  of  B  and  H.  It  is  proved  by 
the  approximations  of  geometr}^  obtained  by  the  proper- 
ties of  straight  lines,  that  C  and  G  are  each  greater  (much 
5152 


greater)  than 


6561 


parts  of  B  and  H,  and  less  (rriuch  less) 


than 


5154 


;  therefore  {Rcdiictio  ad  absurdtim),  they  shall 


6561 

5153  • 

be  each  2~r  t  because  they  can  be  nothing  else,  there  being 

no  other  6561  part  between  5152  and  5154. 

"  The  proposition  is  therefore  demonstrated  ;  and  the  frac- 
tional area  of  one  square,  which  is  equal  to  one  circle  (the 
area  of  each  being  one),  is  6561,  and  the  fractional  area  of 
one  circle  inscribed  in  such  square  is  5i53*" 

The  expression,  "  It  is  proved  by  the  approximations  of 
geometry,  obtained  by  the  properties  of  straight  lines," 
contains  a  very  subtle  allusion  and  meaning.  Mr.  Parker 
approves  the  approximate  value,  as  obtained  by  Playfair, 
after  the  method  of  its  obtainment,  viz.,  by  the  properties 
of  straight  lines,  where   such  lines  are  defined  as  being 


20  Parker's  Quadrature  of  the  Circle.        §  2. 


without  breadth  or  thickness.  Assuming  the  property  of 
breadth  to  a  line  or  unit  of  measure,  or  obtaining  the  value 
of  it  by  means  oi  area  computation^  works  a  change  on  the 
Playfair  result  necessarily.  Now,  if  Mr.  Parker  is  cor- 
rect in  his  taken  relation  between  triangle  and  circle  to 
obtain  a  least  integral  unit  of  measure — i.  e.,  the  number 
3 — then,  without  at  all  conflicting  with  the  Playfair  results, 
his  own  are  right,  if  Playfair's  are  so.  (See  Reflections 
on  the  Quadrature,  §  7.) 

'"'•  Proposition.  XII. 

"  The  true  ratio  of  circumference  to  diameter  of  all  cir- 
cles is  four  times  the  area  of  one  circle  inscribed  in  one 
square  for  the  ratio  of  circumference,  to  the  area  of  the 
circumscribed  square  for  the  ratio  of  diameter.  And 
hence  the  true  and  primary  ratio  of  circumference  to  di- 
ameter of  all  circles  is  20612  parts  of  circumference  to 
6561  parts  of  diameter." 

"  It  will  be  known  that  if  the  diameter  of  the  circle  G  in- 
scribed in  H=i,  then  the  area  of  H  also=i.  It  will  be 
known,  also,  that  the  area  of  G  equals  half  of  the  circum- 
ference   multiplied    by  half   the    diameter,   and   ixj=i; 

hence,  the  diameter  of  G  being  one, 
then  the  area  of  G  equals  \  its  cir- 
cumference, and,  vice  versa,  the  cir- 
cumference of  G  equals  four  times  its 
area.  And  the  diameter  of  G  being 
one,  it  therefore  equals  the  area  of  H, 
because  the  area  of  H=i.  There- 
fore, the  first  part  of  the  proposition 
is  demonstrated,  and  four  times  the  area  of  any  inscribed 
circle  for  a  ratio  of  circumference,  to  the  area  of  the  cir- 
cumscribed square  for  a  ratio  of  diameter,  is  seen  to  be  a 
true  ratio  of  circumference  to  diameter  of  all  circles. 

"  It  has  been  proved  (Proposition  XI)  that  by  the  primary 
relations  existing  between  straight  lines  and  curved  lines, 
as  developed  by  the  opposite  ratio  of  the  equilateral  trian- 
gle and  the  circle,  the  fractional  area  of  11=6561,  and  the 


§  3*  Quadrature  by  Peter  Metius.  21 

area  of  6=5153  ;  therefore,  the  true  and  primary  ratio  of 
circumference  to  diameter  of  all  circles=4  G,  for  the  ratio 
of  circumference  to  the  area  of  H  for  tiie  ratio  of  diameter  ; 
and  since  0^:5153,  and  H— 6561,  therefore  the  true  and 
■primary  ratio  of  circumference  to  diameter  of  all  circles 
^=5153X4=20612  parts  of  circumference  to  6561  parts  of 
diameter." 

"  The  proposition  is  therefore  demonstrated,  and  the 
quadrature  of  the  circle  is  demonstrated."  Mr.  Parker 
should  have  added,  to  be  explicit,  and  exceptional  to  the 
Playfair  method,  "  by  way  of  area  computation." 


QUADRATURE  BY  PETER  METIUS. 

(§3.)  Some  years  ago,  while  examining  into  the  rea- 
^  soning  of  Mr.  Parker,  the  author  found  notice  of  the  ratio 
of  Mciius.  He  wrote  Mr.  Parker,  asking  him  if  he  was 
acquainted  with  the  grounds  on  which  Metius  obtained  it. 
He  replied  that  he  was  not ;  but,  upon  testing  the  ratio 
sent  by  his  own,  he  found  some  very  curious  numerical  re- 
lations of  difference.  Subsequently,  in  a  proposed  second 
edition  of  his  work  (published  after  his  death),  he  notices 
this  ratio  and  these  relations  as  follows  : 

"  The  ratio  of  Metius,  known  for  more  than  a  century 
past  (113  to  355),  is  the  nearest  approximation  to  the  truth 
ever  made  in  whole  numbers  ;  but  it  does  not  answer  the 
imperative  law  contained  in  our  twelfth  proposition,  and 
therefore  it  can  not  be  true.  The  circumference  can  not 
be  divided  by  four,  without  a  fraction  or  remainder.  By 
whatever  means  Metius  may  have  obtained  his  ratio,  its 
examination  shows  it  to  be  of  the  same  composition  as 
mine,  but  improperly  divided.  For  example,  if  113  shall 
be  the  diameter  of  a  circle,  then  circumference   (355)   is 

— -? —  part   too    little.     But    if  355  shall    be    the    circum- 
ference of  a  circle,  then  diameter  (113)  is  .   .    too  big.     It 


22  Parker's  Quadrature  of  the  Circle.        §  4. 

thus  affords  a  very  perfect  evidence  that  my  ratio  20612  to 
6561  is  the  true  one,  as  we  have  fully  proved  it  to  be." 

The  conchision  thus  drawn  does  not  seem  to  be  so  mani- 
fest as  stated.  The  relation  between  the  two  ratios  is, 
however,  very,  yes,  exceedingly  remarkable,  as  the  state- 
ment will  show  : 

2061 1 
20612    :    355    ::    6561    :    112 


6561    :    113    ::    20612    ;    355 


20612 

I 


6561 


(Mr.  Parker  has  confused  the  results.)  The  relation 
seems  to  be  one  which  has,  at  some  time,  been  found  as  a 
variant  on  the  Parker  forms,  because  of  showing  the  same 
composition,  as  he  says.  The  reverse  of  the  case  will  not 
hold  ;  for,  if  the  Parker  forms  be  tested  by  those  of  Melius, 
no  similar  relation  will  be  found  to  exist ;  therefore,  it  would 
seem  that  those  of  Melius  were  derived  from  those  of  Mr. 
Parker. 


SECTION  II. 

REFLECTIONS    ON   THE    QUADRATURE   BY   MR.    PARKER. 

(§4.)  It  is  averred  that  the  quadrature  by  Mr.  Parker 
is  of  great  value.  It  is  not,  however,  because  of  the  in- 
trinsic value  of  his  work  that  it  is  so  largely  set  forth  ;  nor 
is  it  from  any  immediate  motive  to  advocate  or  sustain  it. 
It  is  (i)  because  his  can  be  shown  to  be  that  identical  meas- 
ure which  was  used  anciently,  as  the  perfect  measure,  by 
the  Egyptians,  in  the  construction  of  the  great  pyramid, 
which  was  built  to  monument  it  and  its  uses;  (2)  because, 
from  it,  the  sacred  cubit  value  was  dej'ived,  which  was  the 
cubit  value  used  in.  construction  of  the  Temple  of  Solomon, 
the  Ark  of  Noah,  and  the  Ark  of  the  Covenant — the  value 
of  all  which  consisted  in  the  value  of  the  measures  used ; 
(3)  because  it  affords  that  kabbalistic  value,  which,  before 
all  others,  conveys  in  the  Bible  the  idea  of  God,  the  mean- 


§  5-  Reflections  on  the  Same.  23 

inrr  of  the  term,  and  the  value  of  His  works  in  the  Cosmos  ; 
(4)  because  the  geometrical  symbols  out  of  which  it  is  seen 
to  spring,  with  their  primary  numbers,  are  seen  to  have  a 
kind  of  elemental  relation  to  each  other ^  and  were  made 
use  of  in  the  mysteries  to  convey  the  esoteric  teachings; 
and,  finally,  (5)  because  it  appears  bound  up  in,  and  as 
making  a  fundamental  part  of,  the  British  system  of  long 
and  land  and  time  measures.  If  these  statements  are  true, 
there  will  admittedly  be  no  use  to  assert  that  it  is  well 
worthy  of  being  set  forth.  All  who  appreciate  the  intense 
labor  of  research  for  light  upon  these  matters  will  attach 
a  value  to  this  work  of  Mr.  Parker  far  beyond  that  of  the 
standard  method,  even  though  it  should  be  defective,  be- 
cause its  value  will  consist  in  its  being  a  literary  key,  such 
as  has  never  yet,  it  is  thought,  rewarded  the  generations 
upon  generations  of  searchers  in  the  Bible,  in  mythology, 
and  in  the  antiquarian  fields.  In  this  view,  the  question 
simply  of  its  mathematical  value  is  one  of  the  least  possi- 
ble importance  as  a -primary  one;  although  once  recognized 
to  have  been  used  as  stated,  there  is  no  doubt  but  that  it 
would  cause  the  foundations  of  the  standard  methods  to  be 
reviewed  with  an  intensity  of  thought,  which  might,  per- 
haps, in  the  end,  establish  Mr.  Parker's  method  as  the  one 
giving  a  more  useful  result — i.  e.,  perhaps,  such  an  inte- 
gral one,  in  area  computation,  as  could  be  followed  or 
copied  after  in  material  construction ;  albeit,  it  might, 
just  as  the  Playfair  method,  be,  after  all,  but  an  approxi- 
mation. With  this  apology,  it  may  be  well  to  suggest  some 
thoughts  in  relation  to  this  quadrature  value,  which,  to 
some  extent,  are  worthy  of  attention,  and,  to  some  extent, 
are-  curious. 

MR.  Parker's  quadrature  values  obtained  by  area  com- 
putations. 

(§  5.)  It  seems  to  be  of  importance,  and  it  will  be  ob- 
served, that,  from  beginning  to  end,  Mr.  Parker  seeks 
the  quadrature  through  area  measure,  in  terms  of  area, 
and  finally  obtains  his  numerical  value  of  rectification  by 


24  Parker's  Quadrature  of  the  Circle.         §  6. 

an  area  computation.  His  numerical  values  are  all  area 
values  to  correspond  with  his  geometrical  figures ;  and 
even  so  in  this  final  value,  for  it  is  in  area  terms  where  it 
exhibits  a  necessary  value  of  linear  measure  of  circumfer- 
ence. This  being  the  case,  it  is  evident  that  his  computa- 
tions are  susceptible  of  material  realizations,  as  in  object- 
building  or  copying.  If  his  process  is  correct,  then,  under 
his  Proposition  XI,  he  has  raised  a  test  by  which  to  work 
a  change  on  the  standard  method  to  make  it  conform  to 
area  conditions  and  requirements.  The  fact  that  independ- 
entl}'  he  has  reproduced  exactly  the  same  forrrjulse  which 
the  ancients  had,  which  formulae  had  with  them  application 
to  the  same  common  end,  viz.,  relation  of  diameter  to  cir- 
cumference, goes  far  to  prove  that  his  steps  of  ascertain- 
ment must  have  been  the  same  as  with  them,  though  they 
may  have  had  other  and  more  satisfactory  methods  of  illus- 
trating and  enforcing  the  result.  His  process  seems  to  de- 
pend for  its  correctness  upon  the  Tightness  of  his  ground  of 
the  opposite  qualities  of  the  triangle  and  circle.  If  this  is 
rightlv  taken,  his  numerical  integral  relation  founded  on 
the  number  3  must  be  right.  His  final  step  for  obtaining 
the  area  5153  of  the  inscribed  circle  depends  upon  the 
question  whether  the  JLcgendi'e,  or  Playfair  approximate, 
is  right  as  a  transcendental  one. 

CURIOUS      FEATURES     OBSERVABLE      IN      THE     DETAILS     OF    THE 

PLAYFAIR    METHOD. 

(§  6.)  It  must  be  known  that  the  results  as  to  the  value 
of  >T,  by  Legendre  and  Playfair,  were  not  of  universal  ac- 
ceptation. They  were,  for  instance,  criticised  as  being 
incorrect,  by  Torelli,  in  the  preface  of  an  edition  of  the 
works  of  Archimedes,  printed  at  Oxford.  Reference  is  made 
to  this  preface,  and  also  to  Playfair's  comments  on  the 
same,  as  they  are  to  be  found  in  the  supplement  to  Play- 
fair's  Euclid.     Torelli  held,  according  to  Playfair; 

"  That  it  is  impossible,  from  the  relation  which  the  rectilineal 
figures  inscribed  in,  and  circumscribed  about,  a  given  curve  have 
to  one  another,  to  conclude  anything  concerning  the  pioperties 


§6. 


Reflections  on  the  Same. 


25 


of  the  curvilineal  space  itself,  except  in  certain  circumstances, 
which  he  lias  not  precisely  described." 

The  following  practical  truths  seem  to  the  author  to  be 
exceedingly  remarkable  as  looking,  in  this  specialized  way, 
toward  the  support  of  Torelli's  assertion,  though  no  asser- 
tion must  be  considered  as  made  that  it  affects  the  truth  of 
the  general  results  of  the  Legendre  method. 

The  burden  of  the  effort  of  Legendre  is  to  show  that  by 
the  growing  diminution  and  equality  between  the  circum- 
scribed C'B'  and  the  inscribed  C  B,  the  curved  line  penned 
up  between  them  becomes  measurable  ;  which  curved  line, 
at  any  stage  of  bisection,  being  an  even  and  known  part  of 
the  whole  circle,  from  it  the  length  of  the  entire  circumfer- 
ence, and  consequently  the  area  of  the  curved  space,  is  to 
be  had.  The  measure  of  this 
growing  equality  is  always  to  be 
tested  by  the  difference  of  value, 
at  any  stage  of  bisection ,  between 
CBand  C'B'.  In  the  diagram, 
which  may  stand  for  any  stage 
of  bisection,  C  B'  is  the  chord  of 
half  the  arc,  and  therefore  E  E' 
is  B  B'  for  every  succeeding  bi- 
section. Now,  from  B',  as  a 
center,  with  C  B'  as  a  radius,  de- 
scribe the  arc  C  D.  Then  CD 
will  be  the  quantity  which,  van- 
ishing by  diminution,  the  triangle 
CB'C  will  eventually  become 
CB'D,  and  isosceles;  when  the  curve  lying  between  C  B' 
and  DB'  must,  by  hypothesis,  become  equal  to  CB',  or  to 
DB',  as  a  straight  line.  Now,  as  a  itact,  taking  the  value 
CD  (the  difference  between  C  B  and  CB')  and  E  E',  for  a 
number  of  bisections,  and  it  will  seem  to  show  that,  with 
relation  to  the  diminution  of  CD,  E  E'  is  increasing,  and 
by  an  increasing  ratio.  It  becomes  a  question,  on  the 
showing,  whether  the  arc  is  not,  relatively,  separating  from, 


26  Parker's  Quadrature  of  the  Circle. 


§6. 


instead  of  approaching,  the  chord.  If  so,  the  question  is, 
what  is  the  effect  of  this  ?  What  does  it  mean  ?  If  E  E'  is 
thus  increasing,  what  is  the  value  of  the  arc  becoming? 
Is  there  some  incompatibility  between  the  geometrical 
conditions,  as  presented  to  the  eye,  and  the  numerical  cal- 
culations of  these  forms?  The  rigid  result  of  such  a  condi- 
tion would  seem  to  be  that,  the  ratio  increasing,  the  step 
would  come  where,  as  Mr.  Parker  avers,  C  B'  curve  would 
necessarily  pass  in  value  beyond  that  of  C'B'  diminished — 
an  absurd  conclusion,  unless  some  unnoticed  incompatibil- 
ity has  existed  between  the  condition  of  the  curve  and  the 
calculations  of  the  sides  of  the  polygons.  It  is  possible 
that  this  may  be  the  case,  since,  in  fact,  the  relations  be- 
tween them  are  not  known,  but  only  inferred.  Practically, 
a  calculation  of  the  value  of  iz  to  6144  sides  of  the  poly- 
gons, taken  from  the  base  that  the  perimeter  of  the  polygon 
of  six  sides  is  one  with  twenty-five  ciphers,  making  the 
radius  one  with  6  repeated  twenty-four  times,  yields  the 
followincr  data  as  to  the  relation  or  ratio  between  CD  and 
E  E',  as  they  respectively  diminish  with  continuing  bi- 
sections of  the  arc : 


6 

sides. 

CD 

12 

(( 

24 

(C 

48 

(« 

96 

<( 

192 

(( 

384 

(( 

768 

(C 

1536 

(( 

EE' 


<( 


0.5706 

1.2404 

2.5301 

5.0847 

IO.I8I8 

20.3697 

40.7426 

:   81.4882 

:  162.9917 

which  shows  a  rapid  ratio  of  diminution  of  CD  with  rela- 
tion to  that  of  E  E' :  and  the  practical  diminution  of  CD 
may  be  judged  of  from  a  statement  of  its  value  at  6  sides 
and  6144  sides,  as  follows  : 

6  sides,  CB'  =  962250448649 

"        C  B' =  862730150341 

CD,  or  difference  =    9952029S308 


§  8.  Reflections  on  the  Same.  27 

6144  sides,  C'B'  =  00085 221 1623 

CB'  =  00085221 1539 

CD,  or  difference  =  84 

which  simply  seems  to  show  that  the  triangle  C  B'C  is  ap- 
proaching to  being  isosceles  unattended  by  a  relatively 
rapid  approximation  of  the  chord  C  B'  to  the  curve  C  B'. 
But  the  relation  of  this  approximation  can  be  had  by  a 
statement  of  the  continuing  ratios  between  B  B'  and  E  E', 
and  these  are  as  follows  ; 

E  E'  for         6     sides     :     B  B'     : 


12 


<( 


"  24        " 

*'  48         "  *.* 


ti 


•   3.93I85I6 

:  3.9828897 
3.9989291 

3-9997322 

3-9999330 
3-9999832 
3-9999958 
3.9999989 

3.9999997 

"  96        " 

*'  192        " 

384 

"         768       <' 

1536 

Does  not  this  simply  show  that  while  the  ratio  of  E  E'  to 
B  B'  can  never  become  i  :  4,  the  ratio  of  CD  to  E  E'  can 
become  i  :  00  large  ?  which  mathematically  expressed 
means  that  the  triangle  CB'C  may  become  isosceles,  while 
yet,  absurdly  enough,  the  chord  and  arc  have  not  as  yet 
assimilated?  Not  only  so,  but  have  separated  by  a,  rela- 
tively, infinite  quantity. 


MATHEMATICS      IS      FAMILIAR    WITH      DEFINITIONS     WHICH      ARE 

UNTRUE. 

(§  8.)  It  is  unfortunate  for  mathematics  that,  in  attempt- 
ing to  set  forth  methods  of  comparative  measures  of  right 
and  curved  lines,  it  has  been  found  necessary  to  assume 
truths  as  the  very  groundwork  of  such  measures,  which, 
in  fact,  and  in  the  nature  of  things,  are  not  so.  As 
to  the  Calculus,  for  instance,  its  results  are  taken  as  exact, 
when  the  differentials,  which  are  real  quantities  belonging 
to  those  results,  are  eliminated;  because,  as  it  is  said,  on 


28 


Parker's  Quadrature  of  the  Circle.        §  8. 


account  of  their  smallness,  they  can  afford  to  be  dropped. 
The  very  inception  of  Newton's  "TVmcz^m,"  for  another 
instance,  is  founded  upon  a  geometrically  false  statement, 
as  regards  exactitude  of  definition — palpably  so.  His 
"  Lemma  I  "  states  :  '•'■^lantities  and  the  ratio  of  quanti- 
ties, which    in    any  finite   time   converge   continually  to 

equality,  and,  before  that  time,  ap- 

c  , — ^ =». —  B      -proach  nearer  the  one  to  the  other, 

than  by  any  given  difference,  ulti- 
mately become  equal."'  Let  AB  C  be 
any  triangle,  and  with  the  length 
AB  as  a. radius,  let  the  arc  B  D  be 
drawn  to  intercept  the  line  A  C. 
Suppose  this  figure,  both  for  trian- 
gle and  segment  of  circle,  be  con- 
tinually and  proportionately  re- 
duced, asAB'C,  AB'D';  \he  rela- 
tive differences  will  never  be 
changed,  and,  consequently,  the  ra- 
tios of  difference  will  always  remain 
the  same.  The  proposition  is  axiomatic,  and  does  not 
require  demonstration.  But  take  the  triangle  ABC, 
with  the  circular  area  ABD,  as  decreasing  toward  AB, 
by  different  and  successive  steps,  one  of  which  is,  say, 
ABE,  with  the  circular  area  A  B  F.  By  this  method,  no 
geometrical  ratio  can  be  preserved.  The  ratio  of  diminu- 
tion has  to  be  calculated  by  numerical  combinations.  But 
there  being  3.  ratio  of  diminution,  in  which  the  difference 
between  the  straight  line  and  the  curve  is,  say,  a  decreas- 
ing one,  it  is,  nevertheless,  plainly  to  be  seen  that  the  only 
equality  of  the  curved  line  B  D  with  the  straight  line  B  C, 
in  any  possible  diminution,  will  be  when  the  line  A  C  shall 
so  close  upon  AB  as  to  wholly  coincide  with  it  (as  to  the 
value  of  their  lengths  now  or  at  last  becoming  alike),  and 
become,  with  AB,  one  and  the  same  line,  at  which  stage 
or  condition  there  can  be  neither  curved  line  nor  straight 
line  left  for  comparison  :  therefore,  so  long  as  those  lines, 
i.  e.,  CB  straight,  and  BD  curve,  exist  at  all,  either  in 


§  9-  Reflections  on  the  Same.  29 

whole  or  in  part,  there  can,  by  possibility,  be  no  equality 
between  them.  Hence,  the  lemma  is  false  in  its  terminol- 
ogy ;  nor  is  it  even  right  in  a  showing  of  a  growing  or 
proximate  equality,  as  regards  the  uliimate  structure  o(  \he 
lines,  as  was  shown  above. 

There  is  a  certain  ridiculousness  in  the  matter,  in  this, 
that  while  the  schools  assert  the  impossibility  of  there  being 
an  integral  relation  between  circle  and  square,  because  of 
the  essential  difference  between  a  curved  and  right  line 
(which  is  true  to  all  intents),  the  possibility  of  this  integral 
relation  is  here,  by  inference,  falsely  set  forth  and  maintained. 
It  is  because  a  line  has  breadth  that  a  curved  and  straight 
line  are  not  comparable.  Straight  and  curved  lines  con- 
ceived of  as  without  breadth  may  be  taken  as  comparable, 
because  of  the  possibility  of  their  reduction  to  points. 

NATURE     SEEMS     TO     AFFORD     CONFIRMATORY    EVIDENCE     THAT 

MR.   PARKER    IS    RIGHT. 

(§  9.)     Mr.  Parker  is  of  opinion  that  there  is  in  numbers 

some,  so  to  speak,  flux  of  notation  of  quantity,  by  which 

geometrical  shapes  can  be  integrally  noted  as  changing  the 

one  into  the  other.     Thus,  if  he  is  right,  there  is  a  unit 

1 
square,  which  is  of  the  denomination  of  7^-—    of  a  square 

area,  while  it  is  also  at  the  same  time  of  a  denomination  of  a 

I 

— — -  of  a  circular  area.     Evidently,  then,  whatever  rectan- 

5153 

gular  figure  isj-epresented  in  terms  of  this  unit  square,  its 

equivalent  circular  area  value  in  integrals  can  be  given  in 

4                                  4 
the  same  terms;  as,  -^^  of  a  square  = of  a   circular 

6561  ^  5153 

area.  It  may  be  that  nature  assumes,  in  some  of  her  prac- 
tical constructions  on  the  principles  of  plane  and  spherical 
geometry,  a  least  cubic  one  ;  and  it  may  be  that  it  is  in 
terms  of  this  least  one  that  she  performs  her  works,  ap- 
^roximating  the  form  of  a  sphere  by  its  use.  It  may  be 
that  Mr.  Parker's  method  is  right  as  a  natural  mechanical 
one,  while  that  by  Playfair  may  be  right  as  a  transcendental 
one.     It  is   certain   that   nature  does  lend   some   data    as 


30  Parker's  Quadrature  of  the  Circle.        §  9. 

touching  some  of  her  methods  of  construction.  The  con- 
dition of  substance  to  form  what  is  called  water,  is  one 
resting  upon  the  quality  of  heat  as  affecting  atomic  particles 
of  matter.  Heat  being  but  a  modification  of  motion  of 
■particles,  a  spheroid  or  drop  of  water  is  such  because  of 
its  particles  being  in  some  peculiarity  of  motion  on  them- 
selves, through  perhaps  the  intervention  of  some  subtler 
substance  in  which  the  atoms  may  act.  Thus  the  globule, 
or  spheroid,  of  water  is  formed.  The  effect  of  cessation 
of  this  motion  is  indicated  by  a  cessation  of  spheroidal 
shape.  Motion  giving  place  to  rest,  the  change  is  charac- 
terized by  change  of  shape;  and  this  change  seems  uni- 
formly to  be  that,  as  to  shape  of  particles,  of  the  equilateral 
triangle  as  part  of  a  hexagon.  On  this  form,  other  shapes 
take  place.  In  one  form,  at  and  growing  out  of  the  cor- 
ners of  the  hexagon,  are  little  squares  or  cubes.  (See  de- 
scription by  Professor  Tyndall  of  these  forms,  as  becoming 
manifested  in  the  breaking  down  of  ice  particles  in  the  in- 
terior of  a  mass,  when  heat  rays  are  passed  through  it.) 
In  this  shape  the  substance  has  become  ice.  If,  chemically, 
the  components  of  water  are  in  integral  atoms,  and  if,  in 
its  structural  form,  in  passing  from  shape  to  shape,  it  passes 
from  one  integral  form  to  another,  as  to  shape,  this  would 
serve  as  a  strong  hint  that  nature  recognizes  the  alliance 
and  interchanges  of  shapes  in  subdivisions  of  wholes  not 
fractions.  It  is  noteworthy  that  the  primary  material  one 
here  indicated  in  ice  seems  to  be  triangular  or  pyramidal, 
then  cubic  ;  and  this  in  a  measure  serves  to  strengthen  Mr. 
Parker's  assertions,  for  it  is  on  the  triangle  as  the  natural 
originator  of  plane  shapes  that  he  raises  a  least  integral  in 
the  number  3,  by  which  to  express  the  value  of  the  circle 
in  terms  of  the  square  and  cube;  and,  again,  he  accom- 
plishes this  by  an  integral  relation,  so  close  to  the  Play  fair 
transcendental  one,  that  the  difference  only  becomes  mani- 
fested at  the  sixth  decimal  place,  in  a  circumference  taken 
to  a  diameter  of  unity. 


§  II.  His  Problem  of  Three  Revolving  Bodies.       31 

SECTION  III. 

PROBLEM    OF   THREE    REVOLVING    BODIES. 

(§  10.)  It  is  thus  seen  that  the  process  of  Mr.  Parker  is 
founded  geometrically  upon  the  elements  of  the  circle  and 
of  the  equilateral  triangle,  being,  as  related  to  each  other, 
the  extreme  opposites  in  nature,  of  which  the  circle  is  tlie 
primary  of  all  shapes,  and  hence  the  basis  of  all  area,  and 
the  triangle  is  the  primary  in  nature  of  all  shapes  formed 
of  straight  lines,  and  of  equal  sides  and  angles.  Of  these, 
the  equilateral  triangle  is  numerically  measurable  ;  and  it 
being  requisite  to  translate  shapes  by  num.bers,  as  to  the 
conditions  required  of  a  least  numerical  integral  value, 
with  which  to  determine  the  value  of  the  circle,  that  inte- 
gral least  number  is  found  to  be  3.  By  means  of  this 
shape  and  this  integral  he  obtains  the  value  of  the  circle, 
that  shape  of  greatest  extension  as  compared  with  the  tri- 
angle, in  terms  of  the  square.  Numerically,  1/  ]/  3  is  op- 
posed by  3-X3-=8i=  diameter  of  his  square,  or  the  length 
of  its  side.  8i"=  656i=area  of  his  square,  in  terms  of  his 
least  numerical  integral.  The  area  of  the  contained  circle 
=5^53  5  and,  by  the  process  set  forth,  changing  area  value 
to  represent  rectification,  diameter  being  6561,  circumfer- 
ence =20612.     The  results,  therefore,  are  : 

(i)     Area  of  square  =         6561  "> 

Area  of  contained  circle  =         5^53  ) 

(2)     Diameter  of  circle  =  6561 


Circumference  of  circle=5 153x4 


0501  ^ 

=20612  5 


PROBLEM    OF    THREE    REVOLVING    BODIES,    BY    MR.    PARKER. 

(§  II.)  Mr.  Parker  follows  up  the  ascertainment  of 
these  data  with  his  problem  of  three  revolving  bodies, 
founded  upon  the  principles  of  the  quadrature.  This 
problem  is  as  follows  : 


32  Parker's  Qt^tadrature  of  the  Circle.      §  ii. 

'•'•Proposition  I. 

"  The  respective  and  relative  motion  of  three  gravitating 
bodies  revolving  together  and  about  each  other  is  as  four 
to  three,  or  one  and  one-third  of  one  primary  circumfer- 
ence. 

"  I  have  always  considered  this  proposition  as  self-evident 
on  the  face  of  it,  and  tliat  no  mathematician  would  deny  it 
and  hazard  his  reputation  on  sustaining  the  denial  with 
proof.  But,  as  I  shall  perhaps  be  called  on  for  proof,  I  add 
here,  at  some  length,  the  solution  of  the  problem,  after  my 
own  method,  as  follows  : 

"  The  problem  of  three  gravitating  bodies  revolving  to- 
gether and  about  each  other  is  one  which,  like  the  quadra- 
ture, has  hitherto  baffled  all  attempts  of  mathematicians  to 
solve.  But  since  this,  like  others  of  the  kind,  is  of  itself 
a  problem,  which  is  daily  performed  and  consequently 
solved  by  the  mechanical  operations  of  nature,  the  failure 
of  mathematicians  to  reach  the  solution  proves  nothing  but 
the  imperfection  of  the  reasoning  applied  to  it. 

"  It  is  a  principle,  I  think,  clearly  demonstrable,  that  what- 
ever can  be  constructed  by  mechanics  out  of  given  magni- 
tudes, can  be  exactly  determined  by  numbers,  and  that 
which  can  not  be  constructed  by  mechanics  out  of  any 
given  magnitudes,  can  not  be  exactly  determined  by  num- 
bers, having  the  same  relation  as  the  magnitudes  one  to 
another.  It  is  for  this  reason,  and  for  this  reason  only, 
that  we  can  not,  out  of  the  same  magnitudes,  construct  a 
square  which  is  just  twice  as  big  as  any  other  perfect 
square ;  neither  can  we  find  the  perfect  root  of  such  a 
square  by  decimal  numbers.  If  this  reasoning  be  true, 
then,  because  the  problem  of  three  gravitating  bodies  is  a 
mechanical  operation  daily  performed  in  nature,  it  is  hence 
a  thing  capable  of  being  proved  by  numbers.  The  great 
difficulty  of  this  problem  has  arisen,  I  think,  from  the  im- 
possibility of  its  full  displa}'  by  diagram,  and  the  difficulty 
of  embracing,  in  any  formula,  all  the  conditions  contained 
in  its  elements.  The  plan  of  exacting  a  display  by  diagram 
of  all  the  geometrical  propositions  is  safe,  and  perhaps  it 


§  II.  His  Problem  of  Three  Revolving  Bodies.       33 

is  llie  onl}^  plan  by  which  the  yet  untaught  mind  can  be 
iniliated  into  the  truths  of  geometry  ;  but  is  it  always  nec- 
essary in  every  original  demonstration?  Are  there  not 
other  means  equally  true  and  equally  safe  in  the  hands  of 
one  accustomed  to  examination,  and  acquainted  with  the 
properties  of  numbers  and  of  shapes?  I  think  there  are; 
and,  without  taking  the  least  unwarrantable  latitude,  or  de- 
parting from  the  clearest  perceptions  of  reason,  I  think 
this  problem  may  be  easily  and  accurately  solved. 

"  The  thing  required  of  every  demonstration  is,  that  it 
shall  give  a  sufficient  reason  for  the  truth  which  it  asserts. 
But,  in  order  that  a  reason  may  be  sufficient^  and  the  con- 
clusion drawn  from  it  safe,  it  is  necessary,  not  only  that 
the  relations  of  cause  and  effect  shall  be  made  clear  to  our 
perceptions,  but  also  that  the  conclusion,  -when  drawn, 
shall  abide  the  test  of  practical  application.  Any  demon- 
stration which  does  less  than  this  can  not  be  relied  on,  and 
no  demonstration  ever  made  has  ever  done  more  than  this. 

"  We  know  very  well  that  things  are  possible  or  impos- 
sible to  be  done,  only  in  proportion  as  the  means  applied 
are  adequate  or  inadequate  to  the  purpose.  We  know  also, 
that  because  different  principles  exist  in  the  various  forms 
of  matter,  therefore  it  is  impossible  to  demonstrate  every- 
thing by  the  same  nieajis  or  same  principles.  It  is  a  narrow- 
minded  prejudice,  therefore,  which  exacts  that  every  dem- 
onstration shall  be  made  by  the  prescribed  rules  of  science, 
as  if  science  already  embraced  every  principle  which  exists 
in  nature.  Yet  none  are  more  frequently  guilty  of  this 
narrow-mindedness  than  mathematicians,  who  often  require 
that  things  shall  be  done  by  the  means  which  the  written 
science  affords,  well  knowing  at  the  same  time  that  such 
means  are  inadequate.  Such  has  always  been  the  case  in 
respect  to  the  quadrature  of  the  circle.  Mathematicians 
have  demanded  that  it  should  be  demonstrated  by  the  prop- 
erties of  straight  lines,  knowing  at  the  same  time  that 
straight  lines  are  inadequate.  Therefore  {and  therefore 
only)  the  thing  has  been  found  impossible,  and  all  other 
demonstrations  are  rejected,  because  they  can  not  be  shown 


34  Parker's  Quadrature  of  the  Circle.      §  ii. 

by  straight  lines.  I  do  not  consent  to  such  unreasonable- 
ness of  decision  ;  but,  in  every  proposition  where  the  suffi- 
cient reason  is  manifest,  I  hold  the  proposition  to  be  demon- 
strated until  it  can  be  disproved. 

*'  In  entering  upon  the  solution  of  the  problem  of  three 
gravitating  bodies,  we  must  first  examine  and  see  of  what 
elements  the  problem  is  composed. 

"  The  elements  which  I  shall  consider  in  this  case,  will 
not  be  such  as  a  mathematician  of  the  schools  would  think 
it  necessary  to  consider.  They  will  be  far  more  simple, 
more  conclusive  (for  such  as  the  schools  can  furnish,  have 
yet  decided  nothing),  and  I  think,  more  comprehensible, 
yet  equally  true  to  nature  (for  I  consult  nature's  laws  only, 
and  not  the  method  or  opinions  of  any  other  man),  and 
equally  accurate  and  precise  with  any  which  can  be  given 
by  any  other  method. 

'■'■h.nA,  first,  each  revolving  body  is  impressed  by  nature 
with  certain  laws  making  it  susceptible  of  the  operation  of 
force,  which  being  applied,  impels  motion.  These  laws 
may  all  be  expressed  under  the  general  \.qx:v[\.  forces,  which, 
though  various  in  their  nature,  possess  an  equalizing 
power,  controlling  each  other  in  such  a  way  that  neither 
can  predominate  beyond  a  certain  limit ;  and  consequently, 
these  bodies  can  never  approach  nearer  to  each  other  than 
a  certain  point,  nor  recede  from  each  other  beyond  another 
certain  point.  Hence  these  forces  are,  <iX  some  mean  foint, 
made  perfectly  equal,  and  therefore  they  may  be  consid- 
ered as  but  one  force,  and  hence  but  one  clement  in  the 
problem. 

'■'•Secondly,  these  revolving  bodies  have  magnitude, 
shape,  density,  etc.,  which  affect  the  operations  offeree  in 
producing  motion.  These  properties  of  revolving  bodies 
have  all  the  same  inherent  power  of  equalization  as  forces. 
For  example,  if  density  be  greater  in  one  than  another,  then 
magnitude  will  be  relatively  less,  force  will  be  less  (the  di- 
rect force),  and  the  momentum  from  velocity  greater,  but 
the  whole  shall  be  equal.     On  the  other  hand,  if  magni- 


§  II.  His  Problem  of  Three  Revolving  Bodies.       35 

tude  be  greater,  and  density  less,  then  force  will  be  greater, 
and  velocity  less,  but  the  whole  shall  be  equal. 

"The  second  element  of  this  problem  may  therefore  be 
comprehended  under  the  term  inagnitude,  which  shall  in- 
clude shape,  density,  and  every  other  quality  or  condition 
which  affects  the  operation  of  force  in  producing  motion, 
and  the  whole  constitute  but  one  element  in  the  problem, 
which  I  term  magnitude ,  as  referring  to  the  bodies  them- 
selves rather  than  to  any  of  their  qualities,  as  density,  grav- 
ity, or  otherwise. 

"  The  third  element  in  this  problem  is  distance,  by  which 
I  would  be  understood  to  mean  the  chosen  distatices  from 
one  another,  at  which  these  bodies  perform  their  revolu- 
tions in  space.  It  is  well  understood,  that  from  the  nature 
of  the  case,  these  revolving  bodies  must  take  up  their  mean 
distances  from  one  another  in  exact  proportion  to  their  re- 
spective magnitudes  and  forces,  and  in  proportion  as  these 
are  greater  or  less,  the  distance  from  each  other  will  be 
greater  or  less.  Hence  it  is  seen  that  the  same  inherent 
power  of  equalization  exists  in  respect  to  distances  as  in 
respect  to  the  forces  and  magnitudes,  and  whether  their 
distances  from  each  other  be  greater  or  less,  equal  or  un- 
equal, they  still  constitute  but  one  element  in  the  problem. 

"  Th.Qfourth  and  last  eletnent  in  this  problem  is  motion, 
or  velocity,  by  which  distances  are  to  be  performed  or  over- 
come by  revolution.  And  here  again,  it  will  be  seen,  that 
because  the  distances  to  be  thus  performed  by  revolution  de_ 
pend  entirely  on  the  chosen  distances  from  one  another,  and 
these  again  depend  on  magnitude  and  force,  therefore  the 
same  equalizing  power  exists  in  regard  to  motion  or  veloc- 
ity, as  exists  in  regard  to  all  the  other  elements,  and  there- 
fore this  also  constitutes  but  one  element  in  the  problem, 
which  I  will  term  velocity,  as  including  momentum,  and 
every  other  quality,  condition,  or  effect  of  motion. 

"  These, _/b?^r  in  number,  are  all  the  elements  necessary 
for  the  mechanical  performance  of  the  problem,  and  con- 
sequently all  that  are  necessary  for  its  determination  by 
numbers;  and  it  has  been  seen  that  such  is  the  nature  of  the 


^6  Parker's  Quadrature  of  the  Circle.      §  ii. 

problem  itselt",  and  the  power  of  these  elements  over  one 
another,  that  every  other  quality  or  condition  affecting 
either,  is  equalized  b}^  and  held  in  subservience  to  these, 
and  these  again  are  equalized  by,  and  held  in  subservience 
to  one  another,  and  all  controlled  by  magnitude,  so  that  the 
whole  constitute  but  one  -problcni  or  w/rc/^^w/ctz/ operation, 
in  whichybz^r  elements  are  concerned. 

"  The  difficulty  of  reducing  impalpable  things  to  a  pal- 
pable standard  of  measure  is  generally  conceded  ;  but,  in 
this  case,  I  think  the  difficulty  does  not  exist,  and  that  these 
elements  may  all  be  as  truly  represented  by  numbers  and 
magnitudes  as  if  they  were  palpable  things  in  themselves, 
having  the  qualities  of  length,  breadth,  and  thickness.  For 
example,  let  a  stone  be  a  magnitude,  having  shape,  bulk, 
density,  etc.  Now,  a  force  which  can  raise  this  stone 
one  foot  from  the  ground,  and  hold  it  suspended  there,  is, 
in  its  relation  to  the  magnitude  or  stone,  exactl}'  equal  to 
one  foot  of  measure;  and  because  the  stone  is  held  sus- 
pended, and  does  not  descend  again,  nor  rise  higher,  it  is 
evident  that  the  force  and  magnitude  have  become  equal  at 
that  ^oint  of  elevation ,  and  therefore,  vice  versa,  the  mag- 
nitude or  stone  is,  in  its  relation  to  the  force,  exactly  equal 
to  one  foot  of  measure,  and  consequently  distance  and  mo- 
tion are  each  also  seen  to  be  equal  to  one  foot ;  and.  the 
same  principles  of  applicability  to  measure  exist  in  three 
bodies  suspended  in  space,  and  made  to  revolve  about  each 
other  by  forces  inherent  in  themselves.  It  matters  not  that 
other  and  disturbing  forces  exist  outside  or  inside  the  space 
in  which  these  bodies  revolve,  because,  if  another  and  dis- 
turbing force  be  considered,  then  it  ceases  to  be  a  problem 
oi  three  gravitating  bodies  ;  and  also,  because  such  disturb- 
ing forces,  if  they  exist,  operate  proportionally  on  all  three 
of  the  revolving  bodies,  and  in  the  course  of  a  revolution, 
and  consequent  change  of  relative  position,  these  disturb- 
ances must  fnd  their  perfect  equality. 

*'  Now,  let  us  suppose  that  we  have  here  three  bodies, 
revolving  together  in  space  by  their  own  gravitating  power, 


§11.  His  Problem  of  Three  Revolving  Bodies.       37 


f        -^ 

<: 

<c 

^          /         ! 

a 


and  let  the  magnitudes  of  these  bodies  be  exactly  equal  to 
one  another  :  then  their 
forces  shall  be  equal, 
their  distances  equal, 
and  their  velocities 
equal,  and  it  will  be 
seen  that  they  can  not 
revolve  about  each 
other,  but  mw^X.  follow 
each  other  round  a  com- 
mon center,  and  their 
relative  motion,  in  re- 
spect to  any  point  in 
space  (as  the  point  or  star  A)  must  be  on  the  value  of  the 
circumference  of  the  circle  B,  which  passes  through  the 
center  of  each  body,  as  in  the  accompanying  figure. 

"  Now,  let  us  suppose  that  each  of  the  elements  contained 
in  the  problem  of  three  gravitating  bodies,  is  an  equal  por- 
tion of  the  area  of  the  circle  which  these  bodies  describe 
in  a  revolution  ;  then  the  circle  will  be  divided  from  the 
center  into  four  equal  parts,  as  at  the  points  a,  b,  c,  d,  and 
let  each  part  equal  one.  It  will  be  seen  that  in  each  rela- 
tive change  of  position,  each  revolving  body  passes  over 
an  area  equal  to  one  and  one-third.  In  other  words,  their 
relative  motion  is  cis  four  to  three.  So,  also,  if  each  ele- 
ment shall  be  an  equal  portion  of  the  circumference  of  the 
circle  B,  or  an  equal  portion  of  the  square  of  the  diameter 
of  B,  the  same  result  is  manifest,  and  the  relative  motion 
of  each  revolving  body  is  as  four  to  three  of  such  magni- 
tude as  is  made  the  standard  of  measure. 

"Again  :  Secondly.  Let  the  area  of  the  circle  inscribed 
in  the  equilateral  triangle,  whose  sides  make  the  distance 
between  these  revolving  bodies,  be  one,  as  in  the  following 
figure.  It  is  seen  that  the  circle  B,  whose  circumlerence 
these  bodies  describe  by  their  revolution,  is  four  times 
greater  than  such  inscribed  circle.  (See  Plate  XXXI, 
Appendix.)  Hence,  again,  their  relative  change  of  posi- 
tion is  seen  to  be  di?,  four  to  three,  or  one  and  one-third  of 


38 


Parker's  Quadrature  of  the  Circle.      §  ii, 


the   primary  magnitude   which    is   made    the  standard  of 
measure,  and  (Proposition  I,  Chapter  II)  it  is  seen  that  the 

circle  inscribed   in  the 


1 

'          A 
1     / 

1  / 

•  / 
1/ 
1/ 

<; 

i\ 
1  \ 
1  \ 

■  \ 

■  \ 

■  \ 

1     \ 

1                       N^ 
1 

<r 

^     /    ■ 

triangle,  as  above,  forms 
the  basis  of  the  area  of 
that  triangle,  when  it 
shall  be  measured  by 
circumference  and  ra- 
dius, which  are  the 
only  legitimate  ele- 
ments of  area  in  all 
shapes  alike. 

"x\gain  :    Thirdly.  \\ 
"  is  seen  that  the  equilat- 

eral triangle  [see  preceding  figure],  whose  sides  make  the 
distance  between  these  revolving  bodies,  is  an  angular  shape 
and  being  measured  in  the  usual  way  of  measuring  angu- 
lar shapes,  its  area  equals  the  perpendicular  V  d,  by  half 
the  side.  Now  let  the  perpendicular  P  d,  equal  one.  Then 
it  is  seen  that  the  diameter  of  the  circle  B,  which  these 
bodies  describe  in  a  revolution,  is  one- third  greater  than  the 
perpendicular.  Hence,  in  performing  a  complete  revolu- 
tion, these  bodies  describe  a  circumference  equal  to  one 
and  one-third  the  circumference  of  one  diameter.  \\\  other 
words,  their  relative  motion  is  again  seen  to  be  2,^  four  to 
three  of  one  primary  circumference. 

'■'■Fourthly.  These  bodies,  which  are  revolving  together, 
are  known  (by  hypothesis)  to  be  equal  to  one  another  in 
magnitude,  and  consequently  equal  to  one  another  in  all 
the  elements  concerned  in  their  revolution.  Now,  let  us 
suppose  that  their  distance  from  each  other  equals  one. 
That  distance  is  seen  to  be  the  side  of  an  equilateral  tri- 
angle inscribed  in  the  circle  B,  whose  circumference  they 
describe  in  one  complete  revolution.  [See  preceding  fig- 
ure.] Now,  the  side  of  an  equilateral  triangle  inscribed  in 
a  circle,  equals  the  perpendicular  from  the  base  of  an  equi- 
lateral triangle,  whose  side  equals  the  diameter  of  the  afore- 
said circle  ;  and  therefore,  because  the  square   of  the  side 


§  II*  His  Problem  of  Three  Revolving  Bodies.       39 

of  any  equilateral  triangle  equals  one-third  added  to  the 
square  of  its  perpendicular,  and  because  the  square  of  the 
side  of  the  equilateral  triangle  inscribed  in  B  equals  one^ 
therefore  the  square  of  the  diameter  of  B  equals  one  and 
one-third.  Hence  the  area  of  B  equals  one  and  one-third  the 
area  of  a  circle  whose  diameter  is  one.  Hence,  in  describ- 
ing the  circumference  of  B,  the  relative  motion  of  these 
three  revolving  bodies  shall  be  'dsJ~our  to  three,  or  one  and 
one-third  the  area  of  a  circle  whose  diameter  is  one. 

"By  Proposition  XH,  Chapter  H,  it  is  shown  that  the 
true  and  primary  ratio  of  circumference  to  diameter  of  all 
circles,  which  can  be  expressed  in  whole  numbers,  \s>  four 
times  the  area  of  one  circle  inscribed  in  one  square  for  the 
ratio  of  circumference,  to  the  area  of  the  circumscribed 
square,  for  a  ratio  of  diameter.  [See  preceding  figure.] 
Therefore,  it  is  evident  that  if  the  circumference  of  B  shall 
be  resolved  into  such  primary  parts  as  shall  express  the 
circumference  of  one  diameter  in  whole  numbers,  and  in 
its  exact  relation  to  area  and  diameter,  without  a  remainder 
in  either,  then  the  circumference  of  B  shall  equal  one  and 
one-third  of  one  primary  circumference,  such  as  may  be 
expressed  in  whole  numbers ;  because  the  area  of  the 
square  circumscribing  B  equals  one  and  one-third,  when 
the  side  of  the  equilateral  triangle  inscribed  in  B  equals 
one. 

'■'■  Fifth,  and  lastly.  These  revolving  bodies  must  be  sup- 
posed to  revolve  upon  a  value,  in  which  diameter  and  area 
form  exact  and  equal  portions,  and  the  only  circle  in  nature 
whose  diameter  and  area  are  equal  to  one  another,  and 
identical  in  numbers,  is  a  circle  whose  circumference  is 
four;  hence  the  relative  motion  of  three  bodies  of  equal 
magnitude,  revolving  together,  can  not  be  otherwise  than 
one  and  one-third  of  such  parts. 

"It  is  evident,  from  all  the  foregoing  demonstrations, 
that,  if  we  suppose  the  elements  of  which  this  problem  is 
composed  to  be  magnitudes,  and  take  them  as  a  standard 
of  measure,  whether  such  magnitudes  shall  be  equal  por- 
tions of  the  area  of  a  circle,  or  of  its  circumference,  or  of 


40  Parker's  Quadrature  of  the  Circle.      §  ii. 

the  square  of  its  diameter,  or  whether  we  take  as  our 
standard  of  measure  the  distance  betzveen  these  revolving 
bodies,  which  makes  the  side  of  a  triangle,  or  the  perpen- 
dicular oi  ^wi^  triangle,  or  its  inscribed  circle,  in  all  cases, 
and  in  every  case,  the  relative  motion  of  these  three  re- 
volving bodies  must  be  2iS  four  to  three,  or  one  and  one- 
third  of  such  magnitude  as  is  made  the  standard  of 
measure,  and  there  is  no  other  standard  of  measure  which 
can  be  mathematically  assumed  in  the  premises  which  I 
have  not  here  considered. 

'■'■  The  -proposition  is  therefore  demonstrated  that  three 
gravitating  bodies  of  equal  magnitude,  revolving  together, 
their  relative  motion  shall  be  as  four  to  three,  or  one  and 
one-third  oi  one  primary  circunference. 

"  It  will  be  obvious  to  any  one  that,  in  the  foregoing  dem- 
onstration, I  have  assumed  that  the  magnitudes  of  the 
revolving  bodies  are  all  equal  to  one  another,  and  hence 
their  forces,  distances,  and  velocities  are  all  equal  to  one 
another;  consequently,  they  all  revolve  on  the  same  cir- 
cumference, as  shown  in  the  several  plates,  from  XXII  to 
XXVI ;  therefore,  they  can  not  revolve  about  each  other, 
but  must  foil 021/  each  other  round  a  common  center.  But, 
in  the  problem  of  the  revolution  of  the  moon  about  the 
earth,  and  the  earth  and  moon  together  about  the  sun,  the 
magnitudes  are  all  unequal,  and  hence  their  distances  from 
each  other,  their  forces  and  velocities,  are  all  unequal,  and 
they  are  known  not  to  follow  each  other,  as  in  the  fore- 
going demonstration,  but  to  revolve  about  each  other  in  the 
order  above  stated. 

"It  may  perhaps,  therefore,  be  inferred  that  the  foregoing 
demonstration  is  not  applicable  to  such  gravitating  bodies. 
But  it  must  be  observed,  also,  that  the  equalizing  power  of 
all  the  elements  of  the  problem  are  in  full  force  and  op- 
eration here,  as  well  as  in  the  problem  just  solved,  and 
that  the  chosen  distances,  forces,  and  velocities  are  in  exact 
proportion  to  the  relative  magnitudes  of  the  bodies  revolv- 
ing ;  and  hence  their  relative  motion  shall  be  still  the 
same,  with  this  difference  only,  that  because  the  moon  re- 


§  12.   His  Problem  of  Three  Revolving  Bodies.       41 

volves  about  the  earth,  and  the  earth  and  the  moon  together 
revolve  about  the  sun,  therefore  their  relative  motions  being 
expressed  by  time  (which  is  also  relative),  the  following 
proportions  ensue." 

(§  12.)  While  Mr.  Parker  seeks  to  set  forth  his  own 
clearly  conceived  opinions  that  nature,  in  the  construction 
of  the  solar  system,  and  of  the  cosmos,  founds  all  bodies 
as  to  their  size,  shape,  density,  motion,  relation  to  each 
other,  and  relative  motion  to  each  other,  upon  an  under- 
lyifig  law ,  capable  of  mental  realization  and  of  geometrical 
setting  forth,  by  which,  if  some  one  unit  fact  of  these  phe- 
nomena is  known,  then  all  these  various  elements  may  be 
had  in  a  correlating  and  co-ordinating  method  of  notation, 
he  also  intends  to  say  that  there  is  one,  and  but  one  number 
form,  for  a  flux  through  which  all  these  relations  may  be- 
come manifested  and  known.  The  base  of  the  law  is  the 
relation  of  the  geometrical  elements  of  the  triangle,  the 
circle,  and  the  square  ;  the  second,  or  measuring,  or  no- 
tating,  stage  is  the  relation  of  the  area  and  rectification  of 
the  circle  in  terms  of  the  square.  Now,  these  relations 
may  be  variously  set  forth,  as  of  unity  for  diameter  to 
3. 14159 -(- for  circumference,  and  soon;  but  there  is  but 
one  numerical  form  for  the  expression  of  these  relations, 
through  which  all  these  phenomena  will  correlatively  work 
themselves  out,  and  that  is  in  the  Parker  forms  of  6561  : 
5153X4=20612,  ixnd  none  other ;  and  this  is  the  form  on 
which,  under  his  quadrature  value,  and  his  problem  of 
three  revolving  bodies,  Mr.  Parker  proceeds  to  the  calcu- 
lation of  the  time  periods  of  the  earth  and  the  moon. 

Suppose  that  nature  herself  recognizes  the  division  of 
the  solar  day  into  the  same  subdivisions  that  man  does,  viz., 
5184000'"  (or,  in  other  words,  suppose  that  man  has  been 
taught  these  number  relations  from  nature,  as  by  revela- 
tion, in  what  way  soever  we  may  understand  it  as  coming), 
as  a  time  circle  actually  made  by  the  revolution  of  a  planet ; 
and  suppose  she  herself  has  so  adjusted  her  works  that 
this  circle  has  relation  to  the  abstract  relation  of  square 
area  to  circular  area  and  circular  rectification  in  one  pecu- 


42  Parker's  Quadrature  of  the  Circle.      §  13. 

liar  number  form,  and  none  other,  so  that  she  shall  pre- 
serve harmonious  connection  in  all  her  works,  between 
geometrical  principles  of  change  and  the  power  of  trans- 
lating or  notating  them  through  just  these  number  forms ^ 
and  none  other.  The  conclusion  is  irresistible  that  the 
numerical  methods,  which  we  as  mortals  do  possess,  are, 
after  all,  but  the  very  ones  which  some  unseen  power  has 
been  working  by  in  the  very  creation  of  our  cosmos,  and 
in  some  way  has  actually  implanted  in  us  for  our  use.  The 
test  of  this  is  in  the  application.  Mr.  Parker  has  the  right 
of  comparison  of  two  distinct  forms  of  circular  use.  For 
instance,  a  point  on  the  equator  performs  a  circle  of  time  in 
what  we  call  360  degrees  of  space,  or  24  hours  of  time,  or 
5184000  thirds  of  last  subdivisions  of  time.  Then  5184  is 
the  index  of  this  work  done  and  of  a  circular  value  accom- 
plished. Again,  Mr.  Parker  finds  that  5153  is  abstractly 
the  area  of  a  circle  inscribed  in  a  square  of  an  area  of 
6561.  He  has  the  right  to  institute  whatever  comparisons 
he  sees  fit  between  these  two  relations,  because  of  the  com- 
mon property  which  they  have  of  being  circular  admeasure- 
ments. But  this  is  but  his  right,  and  it  does  not  follow  that 
nature  has  had  any  like  weakness  or  any  like  strength  of 
design.  However,  she  has  a  measure  of  her  own  to  mark 
the  same  time  period,  which  is  in  the  rising  and  setting  of 
the  sun  as  a  fact,  or  in  the  alternations  of  day  and  night. 
If  Mr.  Parker's  uses  are  such  that  nature's  use  is  seen  ac- 
curately to  fit  and  adapt  to  them,  then  instead  of  speaking 
of  "J/r.  Parker's  amplications,'''  we  can  say  and  should  say, 
^^ Nature's  af plications  as  discovered  by  Air.  Parker. '' 

(§  13.)  Mr.  Parker  takes  the  characteristic  value 
of  a  solar  day  as  a  circular  admeasurement  in  its 
division  of  5^S4. 

With  this  he  claims  that,  in  nature,  the  abstract 
value  of  circular  area  is  connected  in  mechanical 
construction,  which  value  is  5^53* 

As  the  one  is  the  solar  day  value  in  thirds,  so  he  makes 
the  second  the  abstract  circular  value  in  thirds,  or  like 
denomination.     He  says : 


§  13-   His  Problem  of  Three  Revolving  Bodies.        43 

"  The  length  of  one  '  circular  clay  '  is  5153000'" 

*'  The  length  of  one  '  solar  day  '  is  5184000'" 

"  The  length  of  one  '  sidereal  day  '  is  5169846'" 

*'  The  difference  between  one  circular  and  one  solar  day 

is  8'  2^"  40'"  (or,  it  is  31-000"',  the  differential  31  being  a 

number  of  great  use). 

"  The  difference  between  one  circular  and  one  sidereal 

day  is  4'  40"  46'"." 

His  relation  of  area  of  square  to  that  of  inscribed  circle 
is  : 

Area  of  square,  6561 

Area  of  inscribed  circle,     5153 
His  relation  of  rectification  is  : 

Diameter  of  circle,  6561 

Circumference  of  circle,  5153X4  =  20612 
His  general  formula  for  the  calculation  of  time  periods, 
under  his  "  problem  of  three  revolving  bodies,"  is  : 

20612X-  =  27482.666+,  and  this  X  -  =  36643.555  +  , 

3  .     ^.  . 

in  which  the  base  is  the  area  of  the  inscribed  circle    X  by 

4  =  its  rectification  ;  the  second  term  is  numerically  the 
value  of  the  moon's  lunation,  and  the  third  is  the  base  of 
the  calculation  of  the  solar  year.  To  illustrate  what  has 
been  said  :  Take  the  second  term  as  the  value  of  the  moon's 
lunation  :  numerically,  it  is  the  value  of  abstract  circum- 
ference, plus  one-third  of  itself,  and  Mr.  Parker  says  of  it 
that  it  is  "  the  value  of  the  moon's  passage  around  the 
earth  over  the  value  of  one  complete  circle  in  space,  in  cir- 
cular days  ;"  that  is,  it  is  in  terms  of  the  abstract  value  of 
5153  and  in  its  denominations,  for  it  was  raised  from  it. 
Reduce  this  to  solar  time,  thus  : 

t^  I S  ^ooo  . 

27482666+X  ^^—^=273183220164+  : 

Take  this  result  as  27.3183220164+  solar  days,  and  reduced 
to  the  proper  divisions  of  solar  time,  there  results  27d.  7h. 
38'  23"  i'"  20"".  Now,  this  result  is  too  small  for  a  sidereal 
lunation  by  the  quantity  4'  40"  46'",  but  strangely  enough, 
or  rather  magnificently  enough,  as  proving  all  that  has 


4-4  Parker's  Quadrature  of  the  Circle.       §  14. 

been  advanced,  this  quantity,  as  will  be  seen  by  reference 
to  the  differences  above,  is  just  the  difference  between  one 
circular  and  one  sidereal  day,  that  difference  being  just 
4'  40"  46'".  Thus  there  are  the  integral  calculations  :  (i.) 
The  Parker  abstract  form,  raised  by  his  problem  of  three 
revolving  bodies,  to  a  numerical  value  of  a  sidereal  luna- 
tion, which,  (2.)  reduced  to  solar  circular  value,  by  the  ad- 
dition of  the  difference  between  the  abstract  circular  value 
and  the  real  sidereal  value  of  a  solar  day,  gives  the  real 
mean  lunation  in  natural  -periods  of  days.  There  could 
be  no  stronger  proof  that  in  our  resultant  number  forms  of 
360  degrees,  24  hours,  and  5184000'",  we  have  simply 
been  making  use  of  a  system  with  which  we  have  had  no 
hand  or  part  in  its  invention.  It  is  to  be  observed  that 
this  result  is  one-fifth  of  one  second  in  a  lunar  month,  less 
than  the  period  given  in  astronomical  time.  But  let  it  be 
remembered  that  from  the  received  astronomical  value,  it 
has  been  inferred  that  with  regard  to  ancient  astronomical 
time,  the  moon's  motion  has  been  accelerated,  and  this  has 
given  rise  to  the  opinion  that  the  solar  system  of  movement 
is  winding  down,  or  closing  up.  By  Mr.  Parker's  time,  on 
this  same  ground,  the  moon's  motion  is  shown  to  be  equable 
and  perfectly  true  to  itself,  going  to  show  that  the  solar 
system  is  not  a  system  of  projectiles,  but  is  a  permanency  ^ 
having  a  far  more  subtle  and  life-like  cause  of  movement. 

The  third  term  of  Mr.  Parker's  application  of  his  prob- 
lem of  three  revolving  bodies,  is  36643.555  +  ,  which  he 
says  is  "  the  exact  value  of  the  earth's  passage  around  the 
sun,  over  the  value  of  one  complete  circle  in  space,  in  cir- 
cular days  ;"  and  on  this  he  proceeds  to  the  reduction  to 
the  exact  period  of  the  earth  in  solar  time. 

(§  14.)  His  periods  of  time  agree  to  a  marvelously 
small  fraction  with  the  standard  periods.  The  following 
tabulation  shows  this : 

(i.)  A  sidereal  lunation. 
Astronomical  time,  27d.  yh.  43'  4" 

By  Mr.  Parker,  27d.  yh.  43'  3"  47'"  20"" 


§  15-  His  Problem  of  Three  Revolving  Bodies.       45 

(2.)  A  solar  liinatio7i. 

Astronomical    time     as    usu- 
ally given,  29d.  I2h.  44'  3" 

84+ 
By  Mr.  Parker,  spd.  i2h.  44'  2"^^ 

The  synodic  period,  as  given 

by    McKay,    the    English 

navigator,  29d.  I2h.  44'  1"  48'" 

By  Mr.  Parker,  29d.  I2h.  44'  2"  50'"  31 


iin 


(3.)  A  mean  year. 

Astronomical  time,  as  given 

*'  thirty  years  since,"  S^Sd.  5h.  48'  49" 

"  By  the  latest  authorities,  as 

taken   from   a  work  of  Dr. 

Dick,"  365d.  5h.  48' 51" 

By  Mr.  Parker,  365d.  5h.  48'  50"  53'"  6"' 

(4.)  A  solar  year. 

Astronomical  time,  S^Sd.  5h.  48'  6" 

By  Mr.  Parker,  365d.  5h.  48'  6"  \"'  6"" 

(§  15.)  These  statements  are  given  to  exhibit  the  use 
made  by  Mr.  Parker  of  his  problem  of  three  revolving 
bodies,  based  on  his  abstract  circular  values,  and  the  use 
of  the  /actors  4  and  3  in  the  formula 

20612X  -  =  27482.66+,  and  this  X  -  =  36643.55+  ; 
3  3 

the  use  of  which  factors  will  be  shown  to  be  very  promi- 
nent in  the  pyramid  works  and  measures. 

And  here,  as  in  relation  to  his  Quadrature,  it  is  stated 
distinctly  that  the  setting  forth  of  the  problems  or  claims 
of  Mr.  Parker  are  not  in  any  way  as  affirming  either  his 
establishment  of  the  Quadrature  or  of  the  problem  of  three 
revolving  bodies.  It  is  absolutely  necessary  to  set  forth  the 
results  of  his  labors,  because  it  will  be  shown  beyond  all 
controversy  that  the  construction  of  the  great  pyramid  was 


46       The  Possibility  on  Mr.  Parker's  Forms     §  16 

WiO.  architectural  display  of  his  results;  and  without  the 
use  of  his  conclusions  and  results,  it  WiW  forever  prove  im- 
possible to  reconstruct  that  mass  agreeably  to  the  concep- 
tion of  the  architect. 


CHAPTER  II. 

SECTION  I. 

THE    POSSIBILITY   ON    MR.     PARKEr's     FORMS    OF    RAISING   A    CO- 
ORDINATING   UNIT    OF   MEASURE. 

(§  16.)  Since  the  value  of  circumference  of  a  circle, 
20612,  is  SO  simply  raised  into  measures  of  time,  the  ques- 
tion arises  :  Why  would  it  not  be  feasible  to  found  upon  the 
same  datum  a  co-ordinating  unit  of  measure  for  other 
purposes?     Take  Mr.  Parker's  formulation: 

20612       4  4X10 

-^^  X  -  -=  27.48266+,  and  this  X -=  366.4355  +  ' 

which  equals 

4                                               4X10 
20.612  X-=  27.48266+,  and  this  X =  366.4355  +  . 

Here  the  first  value  is  an  abstraction,  but  the  second  term  is 
the  value  of  a  moon's  lunation,  and  the  third  term  is  the 
value  of  a  year's  period,  in  circular  days  reducible  by  ob- 
servation to  solar  time  :  and  here  we  have,  as  attached  to 
the  value  of  circumference  in  integrals,  time  measures  in 
natural  periods  of  da^^s.  Suppose  it  is  attempted  to  raise 
from  this  source  a  unit  for  linear,  -plane,  and  solid,  measure, 
in  terms  of  these  elements,  so  as  to  combine  it  with  the  cir- 
cular and  ti^ne  measures.  How  to  do  it?  Very  simply. 
The  natural  unit  for  linear  measure  is  anything  which  will 
serve  as  unity.  That  {ov  plane  and  solid  measures  should 
correlate  with  linear.     Take  the  geometrical  figure  of  the 


§  17-  Of  Raising  a  Co-ordinate  Unit  of  Measure.   47 

cube.  The  edge  of  this  solid  is  a  line,  and  a  line  by  which 
the  superficies  or /"ace  of  the  cube  is  measurable  in  terms  of 
area;  -and  {\\e  face  area  multiplied  by  the  linear  length, 
will  give  the  solidity.  Now,  there  are  twelve  edges  to  the 
cube;  therefore,  divide  the  above  expression  by  12,  and 
there  results 

20^     4  ^  274826+   ^^^  ^1^.^  ^o  ^  3664355, 

12  J  12  3  12 

or, 

X.7X766+  X  ^  =  '^,  and  .his  x  ^  =  ^'S  . 

3  12  3  12 

that  is,  this  ^r5/  terin,  from  whence  spring  these  measures 
of  lunar  and  solar  time,  by  thus  being,  as  it  were,  cubed, 
gives  an  additional  zi7iit  of  measure,  for  linear,  plane,  and 
solid  measure.  If  to  this  first  term,  thus  divided,  some 
■practicable  value  for  use  could  be  assigned,  this  remarka- 
ble co-ordinating  unit  of  measure  would  be  of  the  greatest 
value. 


THIS    possibility,  IN  FACT,  IS  A    REALITY THE    ANCIENT  CUBIT 

AND    BRITISH    INCH. 

(§  17.)  Providentially,  this  first  term  has  a  practicable 
value  assigned  to  it,  so  that  we  are  at  no  loss  as  to  its  rec- 
ognition. For  long,  the  attempt  to  arrive  at  the  value  of 
the  ancient  cubit  measure  has  proved  futile,  except  as  to  an 
approximate  of  what  its  real  length  was ;  that  is,  the 
source  of  its  derivation  has  remained  a  mystery.  Gather- 
ing some  of  the  results  as  to  the  ascertainment  of  this  cubit 
measure,  in  the  '-'■Israelite,'"'  and  in  the  '•'■  Ancient  of  Days,'^ 
the  author  says  : 

"The  value  of  the    ancient    Egyptian    cubit   has  been 
long  sought,  with  results  as  follows  ; 
"  Cubit  of  Elephantine,  20.625  inches,  or  1.7187  +  feet. 
Memphis,       20.47291  "        "   1.70607+    " 
Turin,  20.57869  "        "    i. 71489+     " 

Another,  20.61806  "        "   1.71817+    " 

20.65843  "         "   1. 72153+     " 


(( 


if 


48        The  Possibility  on  Mr.  Parker's  Forms    §  18. 

Another  (Karnak),  20.650  inches,  or  1.7208  +  feet. 

"     Sir  Isaac  Newton,  20.604      "        "   ^-7^7     + 
The  most  important,  as 

ascertained  by  Seyf- 

farth,    on    the    meas-)  20.61113988,     "   1.71759+    " 

ures    of    the    French 

Expedition  of  1799, 

"  These  resuhs  have  been  accurately  taken  from  differ- 
ent authors.  Their  nearness  to  the  trutli  is  sufficient  to 
show  that  the  perfect  determination  of  this  cubit  value  has 
been  obtained  to  wilhin  a  very  narrow  limit;  in  fact,  so 
narrow  that  but  little  hopes  of  further  correction  can  rea- 
sonably be  entertained,  unless  the  very  elemental  principle 
whence  the  cubit  numerical  value  was  derived  be,  in  some 
way,  stumbled  on. 

(§  18.)  "Before  proceeding  to  show  whence  the  de- 
rivation of  the  cubit,  it  may  be  well  to  explain  why  it  is 
stated  that  the  measure  of  Seyfiarth  is  noted  as  the  most 
important.  Seyffarth  was  appointed  to  succeed  to  and  to 
continue  the  labors  of  Spohn  in  the  eflbrt  to  solve  the  ques- 
tion of  translation  of  the  Egyptian  hieroglyphics.  At 
Turin,  in  the  museutti,  he  found  a  papyrus  scroll  containing 
the  ground  plans  and  dimensions  of  the  chambers,  ■passage- 
ways, etc.,  of  the  catacombs  of  Osimandya,  in  Egypt,  as 
to  the  lengths,  breadths,  and  heights  thereof,  in  the  terms  of 
cubits  and  parts  of  cubits.  It  seems  that  the  French  expe- 
dition of  '99  had,  with  great  care,  taken  these  very  meas- 
ures. A  comparison  of  one  with  the  other  was  made,  and 
there  resulted  a  value  of  the  cubit  as  .523524  of  the  French 
meter.  One  meter  =  39-37  inches  English  ;  and  the  re- 
duction gives  20.61113988  British  inches  as  the  resultant 
value.  The  importance  is  that  this  is  derived  from  a  great 
number  of  comparative  measures,  just  as  Sir  Isaac  New- 
ton's was  derived  from  inany  comparative  measures  taken 
by  Professor  Greaves  from  the  passage-ways  and  chambers 
of  the  great  pyramid  of  Jizeh.  As  to  this  value.  Professor 
S.eyffarth  himself  says  : 

" '  There  are  at  present  several  Egyptian  cubit  measures  in 


§  ip.  Of  Raising  a  Co-ordinate  Unit  of  Measure.  49 

Europe  which  agree  with  each  other  in  length  and  divisions.  It 
was,  however,  to  be  decided  whether  those  ells  were  typical  imi- 
tations or  real  instruments  of  measuring.  This  question  was 
answered  by  the  said  ground  plans  at  Turin,  as  has  been  demon- 
strated, with  reference  to  the  Hebrew  cubits,  in  my  "Alphabeta 
y^gyptiacum,  Persarum,"  etc.,  Lipsiae,  1840,  p.  140.  This  work 
forms  the  sixth  part  of  my  "  Beitraege  ?ur  Kenntniss,"  of  which  a 
copy  is  to  be  found  in  the  Astor  library.  The  Egyptian  cubit, 
being  divided  into  3  feet,  7  palmi,  28  inches,  and  several  smaller 
parts  of  an  inch,  measures  o  523524  meters,  i.  e.,  nearly  21  inches 
English.' 

"  Take  the  expression  given  above  : 

.,       4         27.48266  ,    ,  ,  40         266.A7^<i 

i.7i'j66X^=-^-^ h,  and  this  X—  =  ^^ 5:^^  _|_ 

'3  12         ' '  3  12        ^' 

and  here  in  that  very  first  term,  which  is  a  cubing  of  the 

20.612 
value  of  circumference^  or ,  to  raise  a  co-ordinating 

unit  of  measure,  this  ancient  cubit  value  of  the  Egyptians 
is  to  be  found,  with  the  natural  reasons  for  its  derivation. 
With  it  compare 

Value  of  Sir  Isaac  Newton,  i'7i7  f^et. 

Value  of  Professor  Seyffarth,  i. 71759  -f-  feet. 
Obviously ,  then,  we  have  as  a  -practical  fact  that  the  first 
term  of  this  expression  is  the  value  of  the  ancient  cubit  in 
terms  of  the  English  foot  measure.  As  obviously,  the  ex- 
pression from  whence  this  was  derived  was  of  the  value  of 
the  British  inch,  because  it  was  2o6i2-f-i2,  the  reduction 
by  1000  being  made  to  make  it  co-ordinate  with  a  natural 
measure  of  time,  as  stated. 

'■'' Hence,  then,  we  really  and  truly  have  in  the  British 
foot  and  inch  measures  the  identical  derivations  fro?n  the 
eletnents,  and  they  turn  out  to  be  units  of  measure  for 
circular,  linear,  plane,  solid,  and  time  values." 

(§  19.)  Thus,  in  discovering  that  there  is  a  practicable 
value  to  this  unit  of  measure,  co-ordinating  so  many  differ- 
ent kinds  of  measure,  ordinarily  taken  to  be  diverse  and 
distinct  from  each  other,  in  the  Egyptian  cubit  value,  it 
appears  that  the  original  value  whence  this  cubit,  or  cubit- 
ing,  was  taken,  was  itself  utilized,  as  in  British  inches, 


50  The  Parker  Forms  Symbolized  §  20. 

making  it  to  appear  that  the  British  measures  were  prior 
in  rank  to  all  others.  The  further  close  and  intimate  con- 
nection of  these  kinds  of  measure  creates  the  impression 
that  (i)  the  British  system  of  measures  rests  upon  this 
same  quadrature  of  the  circle,  and  (2)  that  the  British 
system  of  long  and  land  measures  is  purposely  framed  to 
answer  at  the  same  time  to  time  measures^  showing  an  ex- 
tension of  the  idea  herein  so  strangely  raised.  Therefore, 
it  is  not  out  of  place  to  assert  that  an  examination  into  the 
structure  of  the  British  system  of  these  measures  may  serve 
to  shed  light  on  the  whole  subject,  and  to  help  the  mind  to 
a  partially  better  conception  of  the  workings  of  the  system. 
This  examination  is  to  be  found  in  Section  III  of  this 
chapter. 


SECTION   II. 


THE  ANSATED  CROSS  OF  THE  EGYPTIANS  AND  THE  CHRISTIAN 
CROSS  THE  EMBLEMATIC  DISPLAY  OF  THE  ORIGIN  OF 
MEASURES. 

(§  20.)  If  it  is  desired  to  display  the  process  of  the 
establishment  of  the  co-ordinating  unit  of  measure  spoken 
of,  by  way  of  symbol,  it  would  be  by  the  figure  of  the  cube 
u7ifolded^  in  co7inection  with  the  circle,  whose  measure  is 
taken  off  onto  the  edges  of  the  cube.  The  cube  unfolded 
becomes,  in  superficial  display,  a  cross  proper,  or  of  the 
tau  form,  and  the  attachment  of  the  circle  to  this  last  gives 
the  ansated  cross  of  the  Egyptians,  with  its  obvious  mean- 
ing of  the  origin  of  measures.  Because,  also,  this  kind 
of  measure  was  made  to  co-ordinate  with  the  idea  of  the 
origin  of  human  life,  it  was  secondarily  made  to  assume 
the  type  of  the  pudenda  hermaphrodite,  and,  in  fact,  it  is 
placed  by  representation  to  cover  this  part  of  the  human 
person  in  the  Hindu  form.  It  is  very  observable  that,  while 
there  are  but  6  faces  to  a  cube,  the  representation  of  the 
cross  as  the  cube  unfolded,  as  to  the  cross-bars,  displays 


§  21.  By  the  Ansated  Cross  and  the  Cross  Proper.  51 

one  face  of  the  cube  as  common  to  two  b(i7's,  counted  as 
belonging  to  either ;  then,  while  the  faces  originally  repre- 
sented are  but  6,  the  use  of  the  two  bars  counts  the  square 
as  4  for  the  upright  and  3  for  the  cross-bar,  making  7  in 
all.  Here  we  have  the  famous  4  and  3  and  7.  The  four 
and  three  are  the  factor  numbers  of  the  Parker  problem. 
But,  what  is  very  much  to  the  purpose  here,  is,  that  the 
golden  candlestick  in  the  temple  was  so  composed  that, 
counting  on  either  side,  there  were  yo?/r  candle-sockets  ; 
while,  at  the  apex,  there  being  one  in  common  to  both 
sides,  there  were  in  fact  3  to  be  counted  on  one  side  and  4 
on  the  other,  making  in  all  the  number  7,  upon  the  self- 
same idea  of  one  in  common  with  the  cross  display.  Take 
a  line  of  one  unit  in  breadth  by  3  units  long,  and  place  it 
on  an  incline ;  take  another  of  4  units  long,  and  lean  it 
upon  this  one,  from  an  opposite  incline,  making  the  top 
unit  of  the  4  in  length  the  corner  or  apex  of  a  triangle. 
This  is  the  display  of  the  candlestick.  Now,  take  away 
the  line  of  3  units  in  length,  and  cross  it  on  the  one  of  4 
units  in  length,  and  the  cross  form  results.  The  same  idea 
is  conveyed  in  the  six  days  of  the  week  in  Genesis,  crowned 
by  the  seventh,  which  was  used  by  itself  as  a  base  of  cir- 
cular measure. 

(§  21.)  On  page  6  of  the  Introduction,  and  in  §  3  of 
the  text,  it  is  noticed  that  with  the  Hebrews  and  in  the 
pyramid — and  this  will  be  shown  hereafter  more  fully — the 
form  of  113  to  355  is  closely  allied  to,  and  intimately  con- 
nected with,  the  Parker  form  of  6561  to  20612.  It  is  so 
in  the  working  out  of  astronomical  and  other  problems, 
and  in  giving  one  great  symbol  value  to  the  Hebrew  god- 
word  Jehovah.  As  seen,  the  symbol  of  the  origin  of 
measures,  from  whence  the  idea  of  the  origin  of  all  things 
took  its  rise,  in  the  number  form,  is  the  cross.  In  Hebrew, 
the,  or  one  of  the,  word  forms  for  '■'■man^^  is  \y^i^,  or  aish. 
The  value  of  this  word  is,  adding  the  values  of  the  letters, 
311,  or,  reading  the  characteristics  of  the  values  as  the 
word  reads,  113 — the  very  diameter  value  in  question.  The 
circumference  value  to  this,  or  355,  is  to  be  found  in  the 


52       The  Parker  Forms  Symbolized     §  22. 

Hebrew  word  for  a  lunar  year,  or  (IJl^,  or  shdnah,  thus 
directly  connecting  the  idea  of  "  man''''  with  an  astronom- 
ical value,  as  also  an  abstract  circular  value.  As  said,  the 
two  values  of  113  to  355  and  6561  to  20612  are,  as  it  were, 
welded  together  in  the  ancient  use.  The  attachment  of  a 
man  to  the  cross  would  be,  in  display,  the  symbol  of  such 
welding.  In  fact,  this  is  a  plainer  and  more  perfect  sym- 
bolization  of  the  ancient  use  than  any  other.  It  was  one 
made  use  of  in  this  form  of  display  by  the  Hindus.  In 
fact,  the  Old  Testament  is  rabbinically  and  kabbalistically 
familiar  with  the  expression  of  crucifying  a  man,  or  men, 
before  the  Lord  and  the  sun.  In  symbol,  the  nails  of  the 
cross  have  for  the  shape  of  the  heads  thereof  a  solid  pyra- 
mid, and  a  tapering  square  obeliscal  shaft,  or  phallic  em- 
blem, for  the  nail.  Taking  the  position  of  the  three  nails 
in  the  man's  extremities,  and  on  the  cross  they  form  or  mark 
a  triangle  in  shape,  one  nail  being  at  each  corner  of  the 
triangle.  The  wounds,  or  stigmata,  in  the  extremities  are 
necessarily ybwr,  designative  of  the  square;  and,  as  in  the 
candlestick,  there  have  been  two  used  as  one,  or  rather  one 
used  as  two,  in  the  connection  of  the  three  nails  with  the 
four  extremities.  The  three  nails  with  the  three  wounds 
are  in  number  6,  which  denotes  the  6  faces  of  the  cube  un- 
folded, on  which  the  man  is  placed  ;  and  this  in  turn  points 
to  the  circular  measure  transferred  onto  the  edges  of  the 
cube.  The  one  wound  of  the  feet  separates  into  two  when 
the  feet  are  separated,  making  three  togethery^r  all,  and 
four  when  separated,  or  7  in  all — another  and  most  holy 
feminine  base  number. 

(§  22.)  The  man's  head  is  the  symbol  of  the  sphere,  or 
circle;  but  this  has  been  enforced  by  the  use  of  a  crown 
upon  it,  of  a  circle  of  light  about  it,  or  of  a  nimbus  or 
glory  radiating  from  it.  In  Hebrew,  the  word  for  head  is 
tJ'NI,  or  rash,  and  reads  213.  The  Hebrew,  so  far  as  the 
author  can  discover,  had  no  expression  for  a  cipher  or 
nought,  but  understood  it  or  not,  as  needed.  Now,  213 
equals  355x6=213-0,  and  this  circumference  value,  as 
that  of  the  head  of  the  man,  is  in  fact  used  to  denote  the 


§  23-  By  the  Ansated  Cross  and  the  Cross  Proper.  53 

subdivision  of  the  circumference  of  355  by  6  diameters 
crossing,  thus  making  the  circle  subdivided  into  12  com- 
partments. This  is  to  be  found  in  the  first  line  of  Genesis, 
and  in  the  picture  of  the  flood. 

(§  23.)  These  are  symbols  of  ancient  use  of  the 
Parker  forms  and  their  connections.  It  serves  but  to  con- 
firm this  use  to  notice  the  conclusion  to  which  Professor 
Seyffarth  arrived  from  the  study  of  the  Egyptian  hiero- 
glyphic signification  of  the  ansated  cross.  It  will  be  ob- 
served that  this  cross,  being  surmounted  by  the  circle,  or 
circular  figure,  in  fact  roughly  represents  the  form  of  a  man, 
with  arms  extended.     Professor  Seyffarth  says  : 

"  It  represents,  as  I  now  believe,  the  scull  with  the  brains,  the 
seat  of  the  soul,  and  with  the  nerves  extending  to  the  spine,  back, 
and  eyes  or  ears.  For  the  Tanis  stone  translates  it  repeatedly 
by  anthropos  (man),  and  this  very  word  is  alphabetically  writ- 
ten (Egyptian)  ank.  Hence  we  have  the  Coptic  ank^  vtia,  prop- 
erly aniina^  which  corresponds  with  the  Hebrew  tJ^1jJ»{,  anosh, 
properly  meaning  anima.     This  J^'^JJi^  is  the  primitive  "1*)^^^  for 

^3JN  ^'^^  personal  pronoun  I).  The  Egyptian  Anki  signifies 
my  soul." 

It  is  curious  that  this  Hebrew  equivalent,  Anosh,  for 
*'  w^a«,"by  Mr.  Seyffarth,  reads  numerically  365 — i,  which 

could  be  intended  to  mean  either  365-1-1=366,  or  365 — 1= 
364,  or  the  time  phases  of  the  solar  year,  thus  shadowing 
forth  the  astronomical  connection. 


54        Primordial  Vestiges  of  these  Symbols.    §  24. 


PRIMORDIAL    VESTIGES    OF    THESE    SYMBOLS. 

Under  the  general  view  taken  of  the  nature  of  the  number  forms 
of  Mr.  Parker,  it  becomes  a  matter  of  research  of  the  utmost  inter- 
est as  to  when  and  where  their  existence  and  their  use  first  be- 
came known.  Has  it  been  a  matter  of  revekition  in  what  we 
know  as  the  historic  age — a  cycle  exceedingly  modern  when  the 
age  of  the  human  race  is  contemplated.''  It  seems,  in  fact,  as  to 
the  date  of  its  possession  by  man,  to  have  been  further  removed, 
in  the  past,  from  the  old  Egyptians  than  are  the  old  Egyptians 
from  US. 

THE    EASTER    ISLES. 

(§  24.)  (i.)  The  Easter  Isles  in  "  mid  Pacific''''  present 
the  feature  of  the  remaining  peaks  of  the  mountains  of  a 
submerged  continent,  for  the  reason  that  these  peaks  are 
thickly  studded  with-  cyclopean  statues,  remnants  of  the 
civilization  of  a  dense  and  cultivated  people,  who  must  have 
of  necessity  occupied  a  widely  extended  area.  On  the 
backs  of  these  images  is  to  be  found  the  "  ansated  cross  " 
and  the  same  modified  to  the  outlines  of  the  human  form. 
A  full  description,  with  plate  showing  the  land,  with  the 
thickly  planted  statues,  also  with  copies  of  the  images,  is  to 
be  found  in  the  January  number,  1870,  of  the  '■'■London 
Builder.'"  The  statues  exhibiting  the  markings  of  the 
cross,  it  is  thought,  are  in  the  British  Museum. 

CRUCIFIED    MAN    IN    SOUTH    AMERICA. 

(2.)  In  the  "-Natiiralistr  published  at  Salem,  Massa- 
chusetts, in  one  of  the  early  numbers  (about  36),  is  to  be 
found  a  description  of  some  very  ancient  and  curious  carv- 
ings on  the  crest  walls  of  the  mountains  of  South  America, 
older  by  far,  it  is  averred,  than  the  races  now  living.  The 
strangeness  of  these  tracings  is  in  that  they  exhibit  the  out- 
lines of  a  man  stretched  out  on  a  cross,  by  a  series  of 
drawings,  by  which  from  the  form  of  a  man  that  of  a  cross 
springs,  but  so  done  that  the  cross  may  be  taken  as  the 
man,  or  the  man  as  the  cross ;  thus  exhibiting  a  symbolic 
display  of  the  interdependency  of  the  forms  set  forth  in 
the  text. 


§  24.    Primordial  Vestiges  of  these  Symbols.         55 


HEBREW    INSCRIPTIONS    IN    THE    AMERICAN    MOUNDS. 

(3.)  A  few  years  since,  a  man  by  the  name  of  Wyrick, 
a  persistent  delver  in  the  squares  and  circles  of  the 
^^mound-builders,'"  at  Newark,  Ohio,  discovered  two  stones, 
covered  with  old  Hebrew  inscriptions.  He  had  borne  a 
very  good  character;  was  a  simple,  unlearned,  and,  by 
reputation,  truthful  man.  Shortly  prior  to  his  finding  these 
relics  in  the  clay  of  a  kind  of- well  or  water  hole,  in  one 
corner  of  one  of  the  inclosures,  he  had  been  in  the  State 
of  Pennsylvania,  and  it  has  been  supposed  that  he  obtained 
these  relics  there,  and  afterward  pretended  to  find  them  in 
the  mounds.  As  to  the  relics  themselves,  they  were  pro- 
nounced upon  by  competent  judges  as  being  of  great  an- 
tiquity, and  certainly  were  made  at  the  expense  of  very 
much  labor,  skill,  and  learning.  While,  by  common  con- 
sent, Mr.  Wyrick  held  the  reputation  of  being  simple  and 
truthful,  the  seeming  impossibility  of  his  alleged  discovery 
made  his  reputation  for  truthfulness,  in  the  estimation  of 
some,  kick  the  beam  ;  and  so,  by  some,  his  Jind  was  put 
down  as  doubtful,  by  sheer  necessity  of  the  case. 

CURIOUS  DATA  REGARDING  THE  MOUNDS  AS  ALIKE  TYPHONIC 
EMBLEMS  WITH  THE  PYRAMID  OF  EGYPT  AND  WITH  HEBREW 
SYMBOLS. 

(4.)  Now,  as  sustaining  his  veracity,  it  is  to  be  seen 
that  there  is  this  very  curious  combination  of  data,  with 
respect  to  these  mounds  :  The  mounds  are  monumented 
circles  and  squares,  or  relations  of  circular  and  right 
line  measure.  To  these  the  Egyptians  and  the  Hebrews 
alike,  were  addicted,  in  the  workings  of  their  hicrhest 
religious  cultus.  Both  the  Egyptians  and  Hebrews  seem 
to  have  derived  their  knowledije  from  the  common  source 
of  the  Phenician.  The  great  pyramid  monumenting  this 
cultus,  stands  on  the  west  bank  of  the  Nile,  the  side  of 
sepulture.  The  books  of  the  Eg3'ptians  containing  this 
knowledge,  were  called  the  boohs  of  the  dead.  The  name  of 


56        Primordial  Vestiges  of  these  Symbols.    §  24. 

3foses,  the  author  of  the  Hebrew  books  containing  this 
knowledge,  was  the  equivalent  of  Thot,  or  Hermes,  the  lord 
of  the  lower  realms,  or  of  the  dead,  who,  also,  was  esteemed 
the  teacher  of  wisdom.  Now,  one  form  of  the  lord  of  the 
descendant,  he  who  held  the  gates  of  death,  was  Typhon  ; 
and  he  was  lord  of  sepulture,  and  his  great  Egyptian  rep- 
resentative was  the  crocodile,  or  alligator,  as  his  Hebrew 
and  Egyptian  representative  was  that  of  the  szvine  or  hog; 
exemplified  in  the  Christian  books  by  the  devil  leaving  the 
man  and  passing  into  the  herd  of  swine,  which  thereupon 
rushed  into  the  sea,  another  emblem  of  Typhon.  Near 
the  Newark  mounds  of  circles,  and  squares,  or  rectilinear 
figures,  is  a  high  hill  overlooking  them,  and  it  is  stated 
that  on  this  hill  is  a  monstrous  mound,  built  to  monument 
the  sha^e  of  aji  alligator  or  crocodile,  apparently  located 
as  lord  paramount  over  the  works  below. 

The  authority  for  this  interesting  crocodile  mound  is  as 
follows,  quoting  from  a  letterof  description  :  "  The  alligator 
of  which  I  spoke  to  you,  I  have  seen  a  great  many  times ; 
is  on  the  farm  adjoining  my  father's ;  is,  as  I  recollect 
it,  from  75  to  100  feet  in  length,  and  properly  proportioned 
as  to  breadth,  length,  and  size  of  legs,  tail,  body,  and 
head  ;  is  distinctly  preserved  and  easily  traced  ;  looks,  as 
I  recollect,  to  the  east,  and  most  of  the  ancient  works  in 
that  vicinity  are  in  an  easterly  direction  from  that  point,  and 
when  the  forests  are  cleared  away,  in  sight  of  the  alligator, 
which  is  on  the  highest  point  in  that  vicinity."  This  de- 
scription is  by  a  very  prominent  and  well-known  public 
man  of  the  State  of  Ohio. 

In  the  city  of  Marietta,  Ohio,  is  to  be  found  some  fine 
remains  of  the  "  motmd-builders .^''  There  is  a  truncated 
cone  surrounded  by  an  elliptical  embankment.  On  one 
side  this  embankment  is  cut  through,  leaving  a  passage-way 
leading  on  to  a  causeway,  raised  above  the  general  level 
of  the  ground,  and  extending  a  distance  of  about  1,000  feet 
to  the  side  of  a  square.  Half-way  across  this  distance,  and 
on  the  general  level  of  the  ground,  a  fire  had  been  made, 
and  gifts  offered,  probably  at  the  dedication  of  the  works. 


§  24.    Primordial  Vestiges  of  these  Symbols.        57 

The  most  remarkable  one  was  a  mass  of  pure  native 
silver  of  four  pounds  weight,  lying  on  charcoal  remains  of 
the  fire  in  which  it  had  been  smelted.  Tliis  metal,  in  its 
pure  condition,  could  only  have  been  procured  from  Lake 
Superior.  It  has  been  noticed  by  those  conversant  with 
the  mounds,  that  the  gifts  (of  dedication)  are  as  follows  : 
Discs  of  mica  slate  from  the  cast  of  the  Alleghanies,  and 
shells  from  the  Gulf  of  Mexico,  or  from  the  south.  Here 
was  silver  from  the  north.  The  west  was  seemingly  not 
represented,  as'  likewise  was  the  case  with  the  Egyptians 
and  Hebrews,  because  the  west  signified  the  Typhonic  por- 
tals into  another  condition  of  existence,  from  whence  no 
gift  could  be  brought. 

MOUNDS    SHOWING    BRITISH    MEASURES. 

(6.)  In  searching  in  the  works  of  Squier  and  Davis,  a 
great  number  of  measures  of  the  mounds  were  found,  and 
it  was  very  observable  that  the  English  measures  seemed 
so  fitting,  that  it  was  difficult  to  free  the  mind  from  dwell- 
ing upon  their  use  in  the  original  construction.  These 
measures  seemed  to  be  multiples  of  3,  4,  6,  and  12,  and 
kept  running  toward  the  value  360.  These  facts  were 
noted  at  the  time  as  curious ;  but  any  possible  connection 
seemed,  even  as  it  does  now,  but  a  wild  freak  of  the  im- 
agination, and  the  matter,  though  noted,  was  dropped. 

AZTEC  OR  "  7nound-builder"  pyramid,  showing   the  use  of 

THE    value    318,    OR     DIAMETER    TO    A    CIRCUMFERENCE      OF 
one^    AS    A    CIVIL    CALENDAR    NUMBER. 

(7.)  It  is  known  that  tradidon  among  the  Aztecs  has 
handed  down  a  very  perfect  account  of  the  deluge  of  Noah. 
Baron  Humboldt  says  that  we  are  to  look  for  the  country 
of  Aztalan,  the  original  country  of  the  Aztecs,  as  high  up, 
at  least,  as  the  42d  parallel  north  ;  whence  journeying,  they 
at  last  arrived  in  the  vale  of  Mexico.  In  that  vale  the 
earthen  mounds  of  the  far  north  become  the  elegant  stone 
P3^ramidal,  and  other  structures,  whose  remains  are  now 
found.     The  correspondence  between  the   Aztec  remains 


58        Primordial  Vestiges  of  these  Symbols.    §  24. 

and  those  of  the  Egyptians  is  well  known.  As  to  the  an- 
cient works,  Atwater,  from  examination  of  hundreds  of 
them,  is  convinced  that  their  authors  had  a  knowledge  of 
astronomy.  As  to  one  of  the  most  perfect  of  the  pyramidal 
structures  among  the  Aztecs,  Humboldt  gives  a  descrip- 
tion to  the  following  eflect : 

"The  form  of  this  pyramid  (of  Papantla),  which  has  seven 
stories,  is  more  tapering  than  any  other  monument  of  this  kind 
yet  discovered,  but  its  height  is  not  remarkable,  being  but  57  feet, 
its  base  but  25  feet  on  each  side.  However,  it  is  remarkable  on 
one  account :  it  is  built  entirely  of  hewn  stones,  of  an  extraordi- 
nary size,  and  very  beautifully  shaped.  Three  staircases  lead 
to  the  top,  the  steps  of  which  were  decorated  witli  hieroglyphical 
scvdptures  and  small  niches^  arranged  with  great  symmetry. 
The  number  of  these  niches  seems  to  allude  to  the  318  sitnple 
and  compound  signs  of  the  days  of  their  civil  calendar.^'' 

318  is  the  Gnostic  value  of  Clirist,  and  the  famous  num- 
ber of  the  trained  or  circumcised  servants  of  Abram. 
When  it  is  considered  that  318  is  an  abstract  value,  and 
universal  ?is  expressive  of  a  diameter  value  to  a  circumfer- 
ence of  u?iity,  its  use  in  the  composition  of  a  civil  calendar 
becomes  manifest.     It  was  in  Hebrew  use. 

OLD    BRONZE    AXES     OF    THE     PHENICIANS,    IDENTICAL    IN    SHAPE 
WITH    THE    COPPER    ONES    OF    THE    MOUND-BUILDERS. 

(8.)  General  Cesnola,  on  the  hillside  of  Idalium,  in 
the  island  of  Cyprus,  exhumed  an  early  Grecian  or  Pelas- 
gic  necropolis,  which  was  three  feet  below  the  surface. 
At  the  depth  of  six  and  a  half  feet  below  this,  a  still 
more  ancient  necropolis  of  the  old  Phenicians  was  found, 
from  which  a  vast  collection  of  their  remains  was  made. 
The  metal  instruments  found  were  of  bronze,  or  an  admix- 
ture of  tin  with  copper.  Among  these,  is  to  be  seen,  in 
this  collection,  in  14th  street,  New  York,  the  style  of  shape 
of  the  axes  used  at  that  time.  Larger  and  smaller,  they 
are  of  the  same  peculiar  shape,  being  solid,  without  any 
hole  for  a  handle.  They  are  identically  the  same  with  the 
copper  axes  to  be  found  in  the  "  mound-bitilders' "  remains. 
These  copper  axes  must  have  been  useless,  because  of  their 


§  25.  British  Long  and  Land  Measures.  59 

softness ;  and,  on  this  continent,  there  was  no  tin  found  for 
admixture.  It  may  have  been  that  there  was  relationship 
of  race  and  nation,  and  these  useless  articles  were  made 
as  mementos  of  the  actual  ones,  which  were,  in  another  part 
of  the  world,  useful  from  the  admixture  of  another  metal. 
The  same  style  of  axes  is  to  be  seen  in  a  Boston  col- 
lection, either  of  Egyptian  or  early  Greek. 

Tlie  above  series  of  facts  seem  to  be  interesting  and 
worthy  of  recital  in  the  connection  made  ;  but  conclusions 
from  them,  as  touching  relation  between  the  Egyptians  and 
Hebrews  and  Phenicians  with  the  "  motmd-buildcrs ,''^  or 
as  touching  the  primordial  use  of  the  Parker  forms,  and 
the  symbols  of  their  use,  are  left  to  the  reader. 


SECTION  III. 

BRITISH    LONG   AND    LAND   MEASURES,  INCLUSIVE  OF   AN   OCCULT 
SYSTEM    OF    CO-ORDINATING    TIME    MEASURES. 

(§  25.)  (i.)  It  is  found  that  the  great  pyramid  can  be  re- 
constructed from  a  standard  base  of  measures  (the  Parker 
elements  of  diameter  to  circumference  values  of  a  perfect 
circle,  viz.,  6561  to  20612  in  inches),  so  that  by  di  j[)iirposed 
variation  on  the  standard,  the  result  is  an  answer  to,  or  is 
in  correspondence  with,  actual  British  measures  of  that 
structure  ;  evidentl}^  to  the  intent  of  the  architect.  (2.)  It 
is  found  that  this  value  of  circumference,  divided  by  1000 

20.612 
and  by  12,  or, ,  is  just  the  value  i. 71766+  of  the 

ancient  Egyptian  or  sacred  cubit,  in  terms  of  the  British 
foot  measure.  (3.)  It  is  found  that  by  the  proportion 
20612  :  6561  ::  i  :  .318309722494-, 
there  results  a  diameter  of  318  -|-  to  a  circumference  of  i  ; 
which  318  is  the  Gnostic  value  of  the  Christ,  and  is  made 
use  of  for  this  meaning  of  diameter,  in  the  318  trained  or 
circumcised  servants  of  Abraham.  It  is  also  found  that 
this  value,  thus  arising,  is,  in  fact,  made  great  use  of  in  the 


6o  British  Long  and  Land  Measures  §  26. 


pyramid,  in  Xhe.  /ormtiI(S  3.18309-j-  X  6=  19.0985  +  ,  and 
190.985+  X  2  =381.970+  ;  the  first  result  being  the  hight 
of  the  king's  chamber,  and  the  second  being  the  half  base 
side  of  that  structure.  (4.)  It  is  found  that  the  means  of 
reconstruction  of  that  mass  is  that  value  of  the  Parker  el- 
ements, which,  from  his  problem  of  three  revolving  bodies, 
gives  the  value  of  a  lunation,  and  of  the  year  period,  in 

circular  time  measure ;  that  is,  the  values  used  are 
.2 
2o6i2Xt2=  36643-55  +  ,  and  this  ^100=  366.4355+ ; 


which  result  is,  as  Mr.  Parker  says,  "the  exact  value  of 
the  earth's  passage  around  the  sun,  over  one  complete  circle 
in  space,  in  circular  days."  (For  the  full  formula,  see  § 
13,  p.  43.)  And,  in  fact,  the  standard  measure  of  the  cir- 
cumference of  the  base  of  the  pyramid  is  36643.55+  inches. 
(§  26.)  (a.)  It  is  found  (§  57),  by  certain  values  taken 
of  the  earth's  diameters,  that  the  difference  between  their 
lengths  in  British  miles,  multiplied  by  this  value  of 
366.4355  +  ,  gives  the  earth's  equatorial  diameter  in  miles; 
that  is, 

(i.)  21.6325+  miles  X  366.4355+ =  7926.9269+  miles. 
The  same  difference,  multiplied  by  the  same  value,  less 
one,  gives  the  other  diameter  taken,  thus  : 

(2.)  21.6325+  milesx  365-4355+  =  7905-2943  miles;  a 
value  greater  than  the  -polar,  and  less  than  the  equatorial 
diameter. 

{b.)  It  is  found  that  this  difference,  stated  in  miles,  is  it- 
self also  a  derivative  from  an  approximate  year  time  value 
in  days,  and  partly  derivable  in  the  same  manner.  An  es- 
timate back  will  clearly  show  the  derivation,  thus  ; 

(i.)   21.6325+  X  (t^X  10^  =  365.04894+. 

It  will  be  observed  that  the  same  process  is  used  as  in 
§  25  (4),  with  the  same  factors,  save  in  the  reverse;  and 
that  here  3^  is  used  in  place  of  3^  Reverse  this  process, 
thus : 

(2.)  365.04894+  ^  Tio  X  M  =  21.6325+  miles. 


§  29-  Include  an  Occult  System  of  Time  Measures.  6i 


Substitute  this  value  in  {a.)  (i.),  and,  by  formulating,  there 
results, 

366.4355+ X  365-04894  .  ,,4'     H    ^     ^    ,     ., 

(3-)  ^^ +  X  -3=  7926.9269+  miles, 

or,  the  equatorial  diameter  of  the  earth  : 

. .  .    365-4355+  X  365.04894+   ,,  4'^      ^     ^  ,      ., 

(4-)  ^^ — X^  =  7905.2943+ miles. 

or,  the  other  diameter  taken. 

(Attention  is  directed  to  the  use  of  the  factors  4  and  3,  as  from 
Mr.  Parker's  problem  of  three  revolving  bodies.  Notice,  also, 
that  the  equivalent  of  144,  as  the  inches  in  the  square  foot  is 
4'^X3^) 

(§  27.)     It  is  found  that  (4.),  in  §  26  (3.),  is  the  same  as  to 

(!•)       365-4355+  X  365-04894, 

as  the  square  of  the  mean  of  these  values.     Substituting 
this  equivalent  expression  of  the  square  of  the  mean  in  that 
formulation,  (4.),  and  there  results  : 
365.24225-'      4^ 
^'^^     ~~[o ^  f^  7905-2943  miles, 

where  the  multiplicand  is  found  to  be  the  mean  solar  year 
value. 

Wherefore,  it  is  seen  that  the  miles  diameter  value  taken 
is  obtainable  directly,  and  the  miles  equatorial  value  of 
diameter  is  obtainable  indirectly,  through  the  square  of  the 
mean  solar  year  value.  With  these  and  additional  data, 
as  of  the  true  solar  year  value,  the  polar  diameter  of  the 
earth  is  to  be  had.      [§57  {d.)  (4.)  and  (5.)  ] 

(§  28.)  The  chiefest  value  in  the  construction  of  the 
pyramid  is  216330,  taken,  first,  as  an  elliptical  property,  or 
difference  of  diameters,  and  was  evidently  intended  as 
the  numerical  value  of  the  difference  of  certain  ones  of  the 
earth's  diameters,  as  21.6330  miles,  for  the  purpose  of  ob- 
taining others. 

(§  29.)  The  consideration  of  the  foregoing  carries  with 
it  the  impression  that  (i)  there  is  a  relation  between  time 
and  British  mile  values,  in  nature's  construction  of  the 
earth,  so  that  (2)  the  material  extension  of  the  earth  in 
miles  is  in  a  kind  of  co-ordinate  relation  with  its  time  meas- 
ure about  the  sun,  and  vice  versa.     So  it  is  well  to  ascer- 


62  British  Long  and  Land  Measures  §  30. 

tain  what,  if  any,  relation  exists  between  time  and  distance^ 
or  area  values,  in  the  British  measures  themselves.  If  such 
a  relation  does  exist  in  them,  and  is  discoverable,  so  as  to 
be  recognizable,  it  certainly  will  serve  to  strengthen  the 
impression  mentioned. 

(§  30.)  That  which  attracts  attention  as  to  the  make-up 
of  the  British  long  and  land  measures  is,  that  after  the  de- 
nomination yards,  or  '■'' three  feet  make  one  yard,''  the  next 
enlargement  is  not  continued  in  whole,  but  in  fractional 
values  ;  as,  "  <^\yards  make  one  rod,""  or,  "  3O4  square  yards 
make  one  square  rod''  Continuing  on,  it  does  not  say  that 
40  square  rods  make  one  square  rood;  then,  that  4  square 
roods  make  one  square  acre;  then,  that  640  square 
acres  make  one  square  mile.  It  runs,  "40  square  rods 
make  one  rood,"  "  4  roods  make  one  acre"  and  "  640  acres 
make  one  square  7nile"  where  the  measures  terminate.  If 
a  special  or  occult  (i.  e.,  one  beyond  the  ostensible  purport) 
measure  can  be  shown  to  run  through  the  grades  of  these 
measures,  having  in  view  some  definite  terminus,  which 
attained  to,  shall  co-ordinate  two  separate  kinds  of  measure, 
then  \\\ii  -principle,  or  such  a  principle,  of  the  structure  of 
these  British  measures,  and  enlargements  thereof,  may  be 
inferred.     It  is  thought  that  this  can  be  shown. 

(«.)  144  square  inches  :=  i  square  foot.  This  gives  a 
square  of  12  divisions  to  the  side.  (4'  X  3^  =  144,  so  that 
16  blocks  of  3  inches  to  the  face,  or  9  blocks  of  4  inches  to 
the  face,  fills  the  square.)  Divide  this  square  into  4  squares  ; 
each  will  contain  6  X  6,  or  ^f)  square  inches,  and  36  X  4  = 


144.  By  this  division,  the  unit  taken  is  a  block  of  6x6 
=  ^^6  square  inches,  4  of  which  is  a  square  foot.  This  is 
the  favorite  subdivision  among  the  ancients,  and  the  basic 
square,  capable  of  subdivision  again  into  blocks  of  3  X  3 
=  9.  Therefore,  take  as  the  base  6  blocks  in  length  of  i 
square  inch  each.  This  use  is  to  be  found  in  the  beginning 
of  Genesis.  {Kabbalistically,  the  measure  of  the  earth  is 
represented  as  in  alternate  black  and  white  squares,  the 
white  signifj-ing  male,  and  the  \Ad,Q^  female.) 


§  31'  Include  an  Occult  System  of  Time  Measures.  6;^ 


(/;.)  36  X  36  square  inches  =  i  square  yard.  '^^6  x  36 
=  1296,  or  6  rows  of  36  X  6,  or  216  X  6=  1296. 

Now,  4  square  yards  =  1296  X4  =  51845  and  this  is  a 
time  measure,  for 

One  solar  day  has  in  hours,  24 

24  X  60'     equals  in  minutes,      1440' 
1440'  X  60"       "        "  seconds,    86400" 
S6400"  X  60'"       "       "  ^/^/yi/5,  5184000'" 
the  characteristic  values  being,  respectively,  24,  144,  864, 
and  5184,  numerically  ;  whereby  it  is  seen  that  the  perfect 
square  of  1^6  inches  to  the  side,  or  the  area  of  one  yard, 
multiplied  by  4,  =:  5184  square  inches,  is,  in  time  value,  the 

-— ,  in  thirds,  of  one  solar  day. 
1000  -^ 

(c.)  Find,  if  possible,  some  condition  of  the  British 
measures,  into  which  this  value  of  one  solar  day  will  evenly 
divide. 

(i.)  I  rod  =  198  inches  to  the  face,  or  198^  =  39204 
square  inches  in  area.     5184  will  not  evenly  divide  in  this. 

(2.)  40  rods  =  \  furlong  in  length,  and  i  rood  in  area, 
and  40X39204=1568160  square  inches  in  area.  5184 
will  not  evenly  divide  in  this. 

(3.)  4  roods  make  cw^^cr^:,  and  1568160  X  4  =  6272640 
square  inches  in  area.  5184  divides  evenly  in  this  1210 
times. 

(§31.)  The  block  used  has  been  6  X  6,  of  36  square 
inches,  or  6  times  the  unit  row  taken,  =  6X1X6;  and 
the  length  of  160  rods,  or  40  X  4?  or  one  acre,  is  just  5280 
of  these  blocks  in  length  by  33  of  them  in  breadth  ;  show- 
ing that  that  condition  which  is  a  -perfect  multiple  of  5184, 

or  of  6"*  X  4,  or  of  the part  of  one  solar  day,  is  ar- 

^  1000  ^  -^ 

rived  at,  when  we  have  a  linear  length  in  land  measure, 

in  blocks  of  36  square  inches  each,  or  of  6  X  6,  of  5280 

numerically  the  mile  value. 

One  rod  face  b}'^  160  rods  deep  is,  in  depth,  one  half  of 

one  mile,  and  320  such  blocks,  placed  together,  make  one 


64  British  Long  and  Land  Measures  §  33. 

mile  in  length.  For  the  ordinary  uses  of  these  measures, 
the  unit  measure  taken  to  begin  with  was  a  block  of  12 
inches  to  the  face,  and  144  square  inches  in  area  ;  doubling 
the  above,  or  160  X  2,  will,  at  the  same  time,  preserve  the 
above  measure  of  time,  in  terms  of  blocks  of  6  X  6,  or  36 
square  inches  each,  and  will  also  give  the  same  numerical 
value,  viz.,  5280,  in  blocks  of  12  x  12,  or  of  144  square 
inches. 

(§  32.)  So,  it  is  seen  that  the  value  of  the  fnile  length 
of  5280  X  33 5  in  blocks  of  6  X  6,  the  mile  being  the  termi- 
nal stage  of  the  table  of  measures,  is  just  that  one  which 
gives  the  Jirst  value  into  -which  the  solar  day  value  will 
evenly  divide.  This  is  very  noteworthy,  when  taken  in 
connection  with  the  facts  and  formulations  hereinbefore  set 
forth,  where  the  solar  year  value,  in  terms  of  solar  days, 
produces  the  values  of  the  earth's  diameters  in  terms  of 
British  miles. 

(§  "^Z-)  (^0  Ox\Q.  acre,  then,  is  5280  blocks  of  6  X  6, 
or  2i^  square  inches  in  area,  in  length,  or  the  numerical 
value  of  the  mile  length  in  terms  of  blocks  of  12  X  12,  or 
144  square  inches  in  area.  And  it  is  the  first  sto^  or  rest, 
where  the  solar  day  value  of  5184  evenly  divides  in  square 
inches. 

Note  that,  In  Hebrew,  stop  or  rest  (equals  also  a  support  or 
base,  as  of  a  system,  applicable  variously)  is  Noah,  or  H^,  and 
our  word  Inch,  literally  changed  into  the  Hebrew,  is  H^"*  or 
I-nch,  the  meaning  of  which  is  yah,  or  Jehovah  is  Noah;  and 
as  the  term  Jehovah,  for  one  of  its  meanings,  is  a  zmit  straight 
one  of  a  perfect  circular  denojninatiofi  (§  82,  b'),  Noah,  by  the 
copula,  is  designative  of  some  unit  foutidation  or  base. 

(b.)  518400'",  or  one  solar  day,  -~  by  60'"  ^86400". 
The  square  yard  contains  6  blocks  of  6  inches  each  to  the 
face,  or,  in  area  ^6  X  36.  One-sixth  (J)  of  the  square 
yard  is  a  block  of  36  X  6  =  216  square  inches.  216  X  4 
=^864  square  inches;  therefore,  864  is  |  of  one  square 
yard,  and  is  the  y^^  of  one  solar  day,  in  seconds. 

Thus,  it  is  seen  that  the  square  yard  seems  to  be  just 
ihat  ;purp)oscd  unit  condition,  such  that  4  even  units,  or  one 


§  2^.  Include  an  Occult  System  of  Time  Measures.  65 

enlarged  square  block  of  four  even  square  yards,  gives  this 
solar  day  number  5184;  hence,  it  would  seem  to  be  the 
source  of  the  co-ordination  of  two  sets  of  different  kinds 
of  measure ;  and  as  it  originates  the  solar  day,  it  may  he 
said  to  be  the  parent  of  the  solar  year,  mmicrically. 

Note  that,  in  Hebrew,  Jared,  the  father  of  Enoch,  is  construed 
to  be  "  tJie  mount  of  descent"  and  is  said  to  be  the  same  with 
Ararat^  on  which  the  cubical  structure  of  Noah,  or  fotindatio?t 
measure,  rested.  Jared,  in  Hebrew,  is  TH"*.  The  root  deriva- 
tions are  the  same  with  those  of  Ararat,  of  acre,  of  earth^^ 
The  Hebrew  "iT^  is  literally,  in  British,  Y  R  D  ;  hence,  in 
Jared,  is  to  be  found,  literally,  our  English  word  yard  (and 
also  I'l"*?  for  Jail,  or  JeJiovah,  is  rod).  It  is  noteworthy  the 
son  of  yared,  viz.,  EnocJi,  lived  365  years  ;  and  it  is  said  of  him, 
by  rabbinical  commentators,  that  the  year  period  of  365  days  was 
discovered  by  him,  thus  bringing,  again,  time  and  distajice  val- 
ues together,  i.  e.,  year  time  descended,  by  co-ordination,  through 
the  yard,  or  Jared,  who  thus  was  its  father,  in  or  through 
Enoch;  and,  truly  enough,  12^6  ^:=  yard  (or  yared)  X  4  =^ 
51S4,  the  characteristic  value  of  the  solar  day,  in  thirds,  which, 
as  stated,  may  be  styled  the  parent,  numerically^  of  the  solar 
year. 

*The  Hebrew  is  noted  for  its  word  stem-building.  The 
methods  of  stem  changes,  to  form  organic  changes,  are  very  in- 
teresting, though  now  not  accurately  known.  '•'■Ararat  =  the 
mount  of  descent  =  "l^'^-in,  Hor-yared.  Hatho  mentions  it 
out  of  composition  by  uXrath  =  jl*l^{.  Editor  of  Moses  Cher- 
enensis  says  :  '  By  this,  they  say,  is  signified  the  first  place  of  de- 
scent (of  the  ark).'"  (Bryant's  Anal  ,  Vol.  IV.,  pages  5,  6,  15). 
Under  '■'•Berge,"  mountain,  Nork  says  of  Ararat :  "  t3"TlKi  for 
ri"1N  (i-  e.,  Ararat  for  Aratlt),  earth,  Aramaic  reduplication." 
Here  it  is  seen  that  Nork  and  Hatho  make  use  of  the  same  equiva- 
lent, in  Arath,  ri")^,  with  the  meaning  of  earth.  Take  the 
word  ■]'1K  =  arad,  to  -proceed  from,  to  be  descended  from, 
which  is  but  a  form  of  -]^»,  or  yared.  Consider  that  "],  t3,  and 
n  are  interchangeable,  and  r)"lKi  arath,  1"^J<(,  arad,  and  t3")J»?, 
arat,  are  cognate  from  a  common  source.  Reduplicate,  and  we 
have,  for  tDlJ^,  arat,  D'T^^{,  or  Ararat.  Consider  that  jl  is  in- 
terchangeable with  n;  and  C^,  and  JlIK,  arath,  becomes  ^"IJ^j 
arets,  the  Hebrew  word  for  earth.     The  Egyptian  word  for  acre, 


66  British  Long  and  Land  Measures  §  33. 

an  earth  measure^  is  ar-ou-a?'^  in  which  there  is  a  simple  redu- 
pHcation  of  '^^{,  ar.  "  ")}«{  =  ar,  is  a  stem  having  the  funda- 
mental signification  oi  ground^  earthy  soil;  h.ence^  yurroivhtg- 
or  f  laughing^  harroiving  or  vexing^  (To  be  found  to  this 
effect  in  "  Origiti  and  Destiny  of  Man."^  Hence,  taking 
the  ^'^1  ar^  as  a  stem,  we  have,  in  vexing  ox  furroxviug^  a  base 
for  the  word  "|"1J«{,  arar^  to  curse^  used  in  Genesis.  Chang- 
ing r")K,  arets^  to  |*")n,  charets^  we  have  to  divide^  separate^ 
to  engrave;  and  in  JJ^")ni  charash,  to  plough,  harrow,  vex. 
Now,  Fuerst  says  that  Tlji},  arad,  is  but  a  form  of  "7")"%  jfared, 
the  woi'd  in  question,  the  }<  and  ^  "frequently  running  into  each 
other."  The  idea  is  descent  from  ^  as  a  source,  also  Jlowing  from, 
for  the  word,  with  suffix,  is  also  a  river.  It  will  be  shown  that 
the  word  T^IJi},  arets,  earth,  is  really  a  very  great  god-xvord,  ex- 
pressive, with  Adam,  D'^^{i  in  the  hifl  participle  of  this  word, 
as  a  verbal,  of  the  first  great  abstract  hermaphrodite  source  of 
production,  or  generation,  or  birth,  or  fowitigfrom^  under  the 
titles  Arts,  Artes,  and  Maditn,  for  Mars:  hence  Arets 
earth,  is  a  term  of  birth  or  descent,  or  of  foivifig  from,  with 
fared  and  Ararat,  while  all  have  reference  to  earth  as  a  source 
of  birth  as  well  as  a  mere  reality.  The  development  under  the 
Afars  form  works  out  the  idea  of  generation,  as  applied  alsa  to 
the  growth  of  civilization — i.  e.,  as  a  source  oi ploughing,  plant- 
ing, building,  measures,  etc.  ;  in  short,  of  all  that  comes  under 
the  generalizing  Ettglish- Hebrew  and  English-Egyptian  word 
Arts.  So,  cognately,  fared  or  Tard,  as  source  or  descent  of 
earth  measure,  is  but  a  form  oi  Aretz,  and  oi  Ararat.  All  this 
seems  to  fasten  the  chief  stem,  from  whence  the  cognate  ideas 
are  derived,  in  the  radical  stem  "){.{,  ar,  with  suffixes,  and  changes 
to  vary  the  original  idea.  In  fact,  Fuerst  says,  under  *ni»s,  arar, 
to  curse,  "  The  stem  is  "^J<^,  and,  in  further  developments,  has 
also  the  harder  sound,  and  so  the  root  {^"IH'  chara,  to  separate, 
sever y  So,  it  is  thus  seen  that  the  words  fared,  Ararat,  aroura, 
arour,  cursing,  arets,  earth,  may  all  be  cognate  forms  under  the 
radical  "^^{,  ar.  It  is  to  be  observed  that  the  numerical  value  of 
the  word  Jared,  or  Tard,  is  taken,  not,  as  usual,  from  any  such 
value  appearing  in  the  word,  but  from  it  as  a  concealed  word  for 
that  measure  here  given  ;  because  of  its  most  curious  connections 
in  relation  to  measures,  and  because  that  it  gives  us  the  very 
English  word  name  (^yard^  under  which  the  very  measure  fitting 
in  these  very  connections  is  numerically  to  be  found. 


§  34-  Include  an  Occult  System  of  Time  Measures.  67 

(c.)    86400" -7- 60"=  1440'.    The  square  foot  contains  144 
square  inches.    Therefore,  the  square  foot  equals  in  inches 

the  —  of  the  numerical  value  of  one  solar  day  in  minutes. 
10  ^  •' 


But  it  is  rather  four  squares  of  6  X  6,  or  of  36  square  inches, 
by  using  the  unit  square  of  6  X  6. 

(^.)  1440'-^  60'=  24  hours,  or  one  solar  day  in  this  di- 
vision.    Therefore,  the  —  partof  one  square  foot  equals  one 

hour,  and  144^-24  =  6  square  inches,  the  basic  unit  value 
from  whence  the  source  of  this  inquiry.  As  this  can  not 
be  formed  into  a  square,  it  is  taken  as  the  even  part  of  the 
unit  square  in  a  row  of  6  square  inches,  as  one  hour,  which 
is  the  geometrical  and  numerical  base  of  the  system  ;  or, 
as  hereafter  to  be  seen,  each  unit  square  of  this  block  of  6 
is  to  be  considered,  by  division,  as  making  four  hours, 
viz  ,  2  of  day  and  2  of  flight. 

Thus  it  is  seen  that  a  system  of  ti7ne  measures  is,  so  to 
speak,  inclosed  in  the  British  system  of  long  and  land 
measures,  the  limits  of  one  being,  or  constituting,  the  limits 
of  the  other  kind — the  difference  being  that,  whereas,  in 
one  kind,  the  measure  runs  from  smaller  to  larger  grades 
of  measure  ;  in  the  other,  it  runs  in  the  reverse,  from  larger 
to  smaller. 

Note,  as  a  matter  for  antiquarians.  Is  it  not  possible  that  the 
British  system  of  measures,  possibly  thus  shown  to  be  of  Phe- 
nician  origin,  is  a  remaining  link  connecting  the  British  people 
with  the  source  of  their  origin,  through  the  Druids?  Their ^/7- 
gals,  and  this  development  as  to  these  measui'es,  seem  to  point 
that  way. 

(§  34.)  It  will  be  shown  hereafter  that  the  two  great  god- 
names,  viz.,  Jehovah  and  Elohim,  in  their  numerical  val- 
ues, stood  (for  one  meaning)  for  a  diameter  and  a  circum- 
ference value,  respectively.  It  is  now  well  enough  to 
state  a  relation  which  one  of  these  names,  in  its  radicals, 
seems  to  have  to  the  measures  under  consideration. 

There  is  a  variation  on  the  Parker  values  of  6561  to 
20612,  used  in  the  pyramid  as  113-f-  to  355-[-,  but  in  the 


68  British  Long  and  Land  Measures.  §  34. 

Bible  it  is  used  as  113  to  355,  whether  as  exhibiting 
this  relation  purely,  or  as  implying  a  decimal,  or  both, 
is  not  as  yet  known  with  perfect  accuracy  of  determina- 
tion. 

The  god-name  Elohim^  or  D\l7K,  has  the  radicals  El, 
7^(,  as  the  stem  masculine,  with  an  //,  or  H,  giving  2^  fem- 
inine quality  attached,  thus  :  El-h,  ^■7^{.  The  numerical 
value  of  7{<  added  is  the  greatly  esteemed  kabbalistic  value, 
or  number,  31.  The  god-name  radical  is  7X?  or  31  ;  but 
there  was  appended  to  it  a  terminative  letter  h,  or  il,  to,  as 
it  were,  finish  out  its  meaning  or  scope,  thus  :  n"*?}<  or  El-h. 
Both  words  were  the  proper  expression  of  the  god-name 
prior  to  that  of  'Jehovah.  The  root,  or  nucleus,  numerical 
value  for  El,  being  31,  with  the  letter  ^,  or  5,  added,  it 
became  36,  or  6^  the  unit  square  referred  to  above.  The 
36  showed  the  system  to  which  reference  was  indicated  by 
the  number  value,  while  the  value  of  the  first  radical,  or 
31,  was  a  DIFFERENTIAL,  uscd  as  a  fiux  between  that  sys- 
tem and  aiiother,  with  which  it  was  essentially  connected. 

The  circular  elements  rediscovered  by  John  A.  Parker 
were  those  on  which  time  and  earth  extension  values  were 
in  nature  based.  Time  values,  and  their  relation  to  earth 
extension  values,  seem  to  have  been  marked  out  through 
a  system  of  measures  founded  on  the  number  6,  and  6x6. 
It  has  just  been  shown  how  such  a  system  involves  and  co- 
ordinates time  and  earth  extension  values.  Now,  Mr. 
Parker,  to  obtain  time  values,  reduces  circular  to  solar 
time,  through  the  intermediation  of  a  unit  of  solar  time 
value,  viz.,  5i84CX)o'",  which,  as  seen,  is  that  value  which 
will  evenly  divide  in  the  numerical  mile  value  of  5280,  or 
rather  of  the  acre  value  composing  it,  and  which  connects 
time  with  British  long  and  land  measures,  as  shown.  Mr. 
Parker's  time  value  circular  is  based  on  the  area  value  of 
the  circle  inscribed  in  the  square,  which  has  been  shown 
to  be  5153.  He  uses  it  as  5153000'",  and  thus,  as  a  perfect 
abstract  circular  value,  contrasts  it  with  the  natural  cir- 
cular, or  solar  day  value  of  5184000"'.     The  connecting 


§  35-         Curious  Chain  of  Linked  Values.  69 

link  between  the  two  systems  of  value,  or  rather  one  such, 
is  the  difference  between  the  two,  and 

5184  —  5153  =  31; 
and  31  is  the  radical  god-word  EL  But  to  El,  or  31,  add 
the  other  radical,  or  ^,  or  5,  and  we  have  El-h,  or  36, 
which  indicates  some  system  of  use,  founded  on  the  factor  6. 
Again,  take  the  limits  of  the  British  measures,  as  shown, 
viz.  : 

144  and  5184. 
Deduct  from  these  values  that  of  EU  or  31,  and  there  re- 
sults 

144  —  31  =  113,  and  5184—31=5153: 
where  one  remainder  is  a  pyramid  and  Bible  value  of 
diameter  to  circumference,  or  113  to  355,  and  another  is 
the  area  of  the  circle  inscribed  in  the  square  of  6561,  and 
at  the  same  time  is  the  value  of  a  circular  day  in  contrast 
with  that  of  a  solar  day.  And  this  shows  the  use  of  this 
diffcre7itial,  as  fluxing,  or  welding,  time  and  earth  meas- 
ures, through  plane  and  circular  foundations. 

Note  to   Chapter  II. 

TABLE    SHOWING    A    LINKING    TOGETHER     OF    VALUES    OF   APPAR- 
ENTLY   INCONGRUOUS    SUBJECTS    MATTER. 

(§  35.)  This  table,  while  given  as  a  curiosity,  because  a  regu- 
larly formed  system  of  use  can  not  be  derived  from  it,  is,  never- 
theless, believed  to  be  of  value  as  the  hint  of  a  well-founded  sys- 
tem anciently  made  use  of  to  correlate,  or  co-ordinate  all  sorts  of 
measure. 

(i.)  Diameter  of  circle,  113;  circumference  of  same,  355; 
113  being  aish  or  man,  and  355  being  shanah,  or  lunar  year. 

(2.)  As  to  the  ancient  Greeks,  Seyffarth,  in  his  "  Chronology," 
page  163,  quotes  as  follows :  "  Theodorus  Gaza  (Petavii  Ura- 
nology,  c.  9),  says  expressly  that  the  ancient  Greeks  had  for  their 
religious  festivals,  a  lunar  year  of  354  days,  but  for  the  civil  life, 
a  solar  year  consisting  of  12  months  of  30  days  each,  with  5,  and 
in  leap  years  with  6,  intercalary  days.  The  same  is  affirmed  by 
Censorinus."  See,  also,  page  168  et  seq.  of  same,  as  to  the  He- 
brews. The  same  statements  hold  good  as  to  the  Egyptians  and 
the  Hebrews.     Agreeably  with  this,  take  the  ancient  scale  of  time 


I 


70  Note  to  Chapter  II.  §  35. 

C-^)  355  (P-)  360         (c.)  365 

^^■)  355  —  I  =  354  (^O  359  (/)  3^5  —  i  =  3%' 

where  on  355  the  shanaJi^  ox  year  word  of  the  Hebrews,  the  in- 
tercalation of  5  days  makes  the  year  of  360  days  (equal  to  the 
celestial  circle  of  360  degrees,  and  the  earth  geographical  circle 
of  360  degrees  ;  also,  the  square  of  6  as  a  factor)  ;  and  the  inter- 
calation of  5  days  on  this  makes  the  full  solar  vague  year  of  365 
days.  It  will  be  observed,  that  by  this  arrangement  the  year  of 
360  stands  as  at  the  mea^i  value  between  the  two  extremes  355 
and  365  ;  the  first  being  an  abstract  value  of  circumference  to 
diameter,  while  the  last  is  the  solar  year  time  circle  in  natural 
periods  of  days.  The  ancient  method  of  display  of  the  year  cir- 
cle was  of  a  serpetit  swallowing  one  or  more  units  of  its  length  : 
so,  under  this  form, 

355—1=354  359  3^5  — 1=3%» 

by  the  reduction  of  one  unit  the  first  scale  is   made  to   show  the 

lunar  years,  viz,  354  days,  which  was  the  number  of  days  of  the 
lunar  year  amo7ig  all  the  ajzcients,  and  364  days  which  was  the 
luni-solar  year  springing  from  the  number  7  [§  90,  §  92  («)],  (and 
here  perhaps,  is  an  indication  of  a  numerical  use  in  "  J-ared"  as 
to  Enoch,  who  lived  365  years,  for  both  "j*)^  and  T^X'  ^<Jded  as 
to  the  character  values,  give  the  number  7).  Thus  it  is  seen  that 
the  form  113  to  355,  is  made  the  base  of  a  scheme  of,  and  is 
linked  in  onto  a  method  of  time  admeasurements  of  two  kinds. 

(3.)  In  the  Hebrew  Bible  there  seems  to  bean  undoubted  con- 
nection between  113  :  355,  and  6561  :  20612.  Taking  the  last 
as  the  standard,  then 

6561   :   20612     ::      113  :  355.0001-j-; 

showing  the  variation  on  355  to  make  this  proportion  good.  How 
these  values  were  worked  to  bring  out  intended  results  is  but  con- 
jectural, but  in  a  measure,  some  of  the  uses  shown  are  probably 
closely  near  the  proper  object.  Now,  in  addition  to  the  above 
forms,  take  the  words  aish,  man,  =;,  numerically,  113,  and 
Adam,  man,  =,  numerically,  144;  which  words  are  thought  to 
be  but  conditions  of  each  other, — ^then 


113  '•  355-OOOI  + 
56-5  :    ^11-5^ 
113  :  3550001  + 


144  :  453.3S93-f- 
72  ;  226. 1946-j- 
36  :    113.0973-f- 


where  now  113  from  a  diameter  value  becomes,  by  a  slight  en- 
largement, a  circumference  value  to  the  form  6  X  6  =  36.  (A  pre- 
cisely same  use  is  worked  on  6561  :  20612  in  pyramid  construc- 
tion.) 


§  35-         Curious  Chain  of  Linked  Values.  71 


And  so  here  we  see  a  shifting  of  use  of  113  from  a  diameter 
value  of  355,  as  founding  a  year  time  scale,  to  a  circumference 
value  of  the  factor  value  6  X  6  =  36,  the  base  of  the  time  and  geo- 
graphical measuring  circles.  And  here  again,  in  36,  the  British 
land  measures  are  linked  to  the  Hebrew  uses  of  113  to  355- 

(As  another  variation  on  this, 

355  :  113     ::     H4  =  45-S3     '■     '440  =  45S-3 

720   :    229. iS-}- 

360  :   114.59+) 

Now,  these  values  as  shown  are  made  use  of  in  the  Bible,  and  in 
the  pyramid. 

(4.)  Take  the  limits  of  the  British  long  and  land  measures, 
viz  : 

(a.)   144  (d.)  51S4; 

where  51S4  is  the  characteristic  of  one  solar  day  in  thirds^  and 
springs  from  144  as  being  the  number  of  square  inches  in  4  square 
yards,  and  51 84  X  121  =  the  limit  factor  of  the  acre.  The  Hebrew 
god -word,  El^  oi'  3I5  gives  this  value  of  31  as  a  difference  value, 
or  link,  running  into  two  systems  ;  for  subtracting  it  from  («.)  and 
((5.),  and  there  results, 

(c.)   113  id?)  5153; 

where,  by  the  use  of  the  differential  El^  or  31,  the  diameter 
value  1 13  is  linked  on  to  the  English  measures,  and  in  such  a  way 
that  at  tJie  sufne  time  5153  is  produced.  Now,  while  113  is  the 
diameter  value  to  a  circumference  of  355,  5153  is  the  value  of  the 
area  of  a  circle  inscribed  in  a  square,  whose  area  is  6561.  Here 
there  is  introduction  to 

The  Parker  forms. 
(5)     ('^■)  Area  of  square,  6561. 

((5.)  Area  of  inscribed  circle,  5153. 
(c.)  Diameter  of  circle,  6561. 
((/.)  Circumference  of  same,  5153  X  4=20612. 
On  these  values  construct  the  formulations  of  Mr.  Parker,  as 
of  his  three  revolving  bodies  : 

(lO  (2.)  (3-) 

20612^  27482.6-f-\  3664355 

X  -  =  ,  and  this  X  -  = 

3  \  3 

6561!  8748.      /  11664-, 

where  we  come  to  the  pyramid  value,  for,  36643. 55  is  in  inches 
the  standard  measure  of  the  circumference  of  its  base,  and 
1 1664  -f-  2  =  in  inches  its  standard  height. 


72  Note  to  Chapter  II.  §  35. 

In  (2.),  27482.66,  as  a  circumference,  equals  the  value  of  a  lu- 
nation, as  shown  by  Mr.  Parker  as  27.48266-I-  days^  to  the  diam- 
eter value  of  874S.  Now,  i  acre  of  5280  blocks  of  6  X  6  lon^, 
by  33  blocks  of  6  X  6  wide,  equals  a  length,  or  number,  numer- 
ically, of  one  niile^  and  equals  in  area  627264  —  o  inches. 

627264  -:-  6  X  6  =::  1 7424. 

17424-^2  :^      8712. 

(Also,  627264 -^- 121  =5184,  the  solar  day  value.)    The  object  is 

to  compare  this  8712  the  even  division  of,  or  —  of,  an  acre,  in 

blocks  of  6  X  6,  with  8748,  the  diameter,  as  shown,  of  a  lunation, 

springing  as  it  does  from  the  Parker  form. 

While  the  use  of  the  god- word  El^  or  31,  as  a  differential^  has 

been  made   above,  the   full  god-word   El-h^  or  36,  can   now  be 

used  as  one  also,  for 

8712") (242 

C--6X6  =  -^ 
8748  3  (  243 

and 

8748  —  8712  =  36: 

that  is,  36  is  the  differential  by  which  the  Parker  forms  for  time, 
based  on  the  relation  of  diameter  to  circumference  of  a  circle, 
can  be  fluxed  into  the  British  measures  (in  square  inches)  of  the 
acre  value,  which  carries  with  it  the  numerical  value  of  the  mile 
as  shown.  6  X  6,  or  36,  the  value  of  the  celestial  circle,  thus  be- 
comes the  differential  of  a  raised  value  of  these  quantities. 

(6.)  But  243  is  equal,  numerically,  to  the  half  the  standard 
height  of  the  great  pyi:amid  in  British  feet,  and  on  a  reduced 
scale  is  found  as  a  measure  of  height  of  the  queen's  chamber. 
There  is  little  doubt  but  that  the  relation  242  is  taken  into  com- 
parative account,  also,  in  the  pyramid  structure ;  if  so,  this  very 
relation  of  differential  comparison  is  a  pyramid  one.  242  is  a 
valuable  number  in  another  way,  for  5184,  the  characteristic  value 

of  a  solar  day  X  121   (or  — )  =627264,  in    inches  the    —    part 

of  the  area  of  one  acre.  This  shows,  that  while  243,  the  pyra- 
mid height,  as  above,  is  adjustable  with  8748  for  divisions  of 
lunar  circles,  243  less  one  (of  a  value  of  36  for  the  ci;z<?),  or  242, 
is  adjustable  with  the  characteristic  of  a  solar  day  value,  to  obtain 
the  area  of  the  acre  in  square  inches. 

The  circumference  of  8748  as  a  diameter  value,  or  27482. 66-|-, 
is  used  in  a  most  remarkable  way  in  the  pyramid,  to  show  a  com- 


§  35-         Curious  Chain  of  Linked  Values.  73 

parison  between  lunar  and  solar  time.  Here  its  diameter,  or 
8748,  affords  a  means  of  contrast  with  a  terminal  land  measure, 
for, 

242  X  6  X  6  =  871 2,  and  this  -f-  36  =  243  X  6  X  6,  or  8748. 

(7.)     Now, 

27482.66)  3664355 

X^  = 
3 
8748.    /  II 664, 

giving  as  a  result  the  standard  measures  of  the  pyramid ;  and 
treating  8748  and  8712  alike, 

8748 i  1 1 664 


871: 

and  1 1664 — 11616=  the  differential  48.  The  height  of 
the  pyramid  is  to  twice  its  base  side  as  diameter  to  cir- 
cumference of  a  circle.  By  the  enlargement  on  the  standard, 
as  will  be  shown,  ^  base  side  is  381.974-I-  feet,  or  a  diameter 
value  to  a  circumference  of  1200.  Twice  the  base  side,  then,  is  a 
diameter  to  a  circumference   of  4800;  and,  as   shown,  48,  the 

—  part  of  this,  is  the  differential  between  a  system  of  time 
100  ^  -^ 

values,  and  a  system  of  land  measure  values,  objectively  resting 

on  the  acre  value,  shaped  for  the  formation  of  a  mile,  as  in  blocks 

of  6  X  6,  giving  the  5280,  or  mile  numerical  value  in  feet,  in  the 

length  of  one  side,  in  blocks  of  6  X  6  inches. 

Thus,  there  has  been   shown  a  curious   method  of  linking  to- 

getlier  of  the  relations 

113  to  355, 

6561  to  20612, 

355        360  365. 

while  all  are  applicable  in  use,  as  exhibited  in  the  measures  of 
the  great  pyramid. 


74  Construction  of  the  Great  Pyramid.        §  26. 


CHAPTER  III. 

SECTION  I. 
INTRODUCTION   TO  THE   CONSTRUCTION  OF  THE  GREAT   PYRAMID. 

(§  26-)  To  a  mind  unbiased  by  the  prepossession  of  a 
theory  that  way,  the  assertion  that  the  great  pyramid  of 
Egypt  was  built  to  perpetuate  a  series  of  measures,  astro- 
nomical and  otherwise,  and  to  contain  a  mathematical  and 
geometrical  system  of  calculation  and  admeasurement,  can 
not  but  be  received  with  incredulity,  and  rightly  so.  Given 
a  great  number  of  pyramids  in  a  land,  the  uses  of  which 
were  notoriously  for  sepulchral  purposes,  and  a  rule  is  es- 
tablished applying  to  all,  unless  proof  to  the  contrary  can 
be  made  as  to  any  one  or  more  isolated  exceptions.  But, 
taking  the  affirmative  of  the  issue,  then  as  to  reconstruc- 
tion ;  given  a  pyramidal  mass,  utterly  destroyed  as  to  its 
exterior  surface,  save  the  corner  base  sockets,  and  a  casing 
stone  in  situ,  with  the  connection  of  the  exterior  with  the 
construction  of  the  interior  lines  seriously  impaired,  to  be 
restored  in  an  original  measure,  which  has  been  lost. 
None  but  proof  of  an  extraordinary  kind  as  to  ability  to  re- 
construct, after  the  mental  conception  of  what  the  architect 
intended  to  represent,  ought  to  become,  or  will  become,  ac- 
ceptable. Tiiis  is  especially  the  case  where  the  time  of  the 
building  of  the  mass  dates  back  beyond  what  may  be  called 
the  historic  age,  and  where  every  theory  advanced  must 
rest  for  support  upon  its  own  intrinsic  merit,  unsupported 
by  positive  evidence  of  any  kind  filtering  through  the  his- 
torical channels  of  the  world. 

Where  a  question  of  measure  is  concerned,  it  will  not  do 
to  cut  and  carve  a  mass,  so  as  to  fit  it  to  such  a  measure, 
particularly  adopted  on  supposition  ;  nor  will  it  do,  as  oc- 
casion requires,  to  change  the  value  of  the  adopted  standard 


§  37*  Introduction.  75 

to  suit  a  stubbornly  resisting  condition  of  the  mass.  It  is 
true  that  this  method  is  the  one  to  be  employed  in  arriving 
at  a  possibility,  or  probability,  as  a  theory ;  but,  this  accom- 
plished, the  further  step  is  required  of  eliminating  all 
theory,  and  all  probability,  and  all  possibility,  leaving  a 
standard  of  measure  as  fixed  and  rigid,  for  instance,  as  is  the 
British  inch.  As  a  sequence  to  this,  the  restoration  of  the 
mass  is  to  be  made  in  terms  and  divisions  of  this  measure. 
Subject  to  these  considerations,  and  they  seem  to  be  fair 
and  pertinent,  if  a  standard  of  measure  can  be  arrived  at, 
as  a  rigid  and  fixed  one,  derivable  from  an  elemental 
source,  by  use  of  which  a  structure  can  be  erected,  as  to 
its  whole  and  most  of  its  parts,  similar  to  that  of  the  great 
pyramid  in  its  geometrical  shapes,  and  in  such  manner  that 
the  evidence  is  convincing  that  the  actual  measure  of  its 
original  construction  is  being  used,  then,  indeed,  the  rec- 
ognition of  that  standard,  its  source,  and  its  use  in  that 
connection,  it  is  thought,  should  be  conceded,  even  though 
the  particularities  of  the  method  of  use  may  not  be  certain. 
(§  37-)  ^^  is  seen  that  from  the  elements  of  quadrature 
of  Mr.  Parker  is  to  be  derived  the  ancient  Egyptian  cubit 
value,  and  that  in  terms  of  the  British  inch  andybot  values. 
Of  the  two  most  important  recoveries  of  the  Egyptian  value, 
viz.,  those  of  Professor  Seyffarth  and  of  Sir  Isaac  Newton, 
that  of  the  last  named  was,  as  has  been  said,  derived  from 
admeasurements  taken  by  Professor  Greaves,  of  Oxford, 
from  the  interior  work  of  the  pyramid.  The  conclusion 
was  that  that  measure  had  been  used  in  the  building  of  the 
structure.  If,  from  the  elements  of  Mr.  Parker, — from 
whence  the  value,  and  reason  of  the  value,  of  that  same 
cubit  measure  is  seen  to  be  derived, — the  pyramid  structure, 
with  the  chief  outlines  of  its  interior  works,  can  be  re- 
stored, with  a  manifest  reason  why  it  was  built, — this 
reason  why  being  an  essential  in  these  very  elements, — it 
will  not  only  be  a  proof  that  the  cubit  value  thence  derived 
was  the  cubit  value,  but  also  that  these  were  the  elements 
whence  it  took  its  rise.  Still  further,  if  it  should  happen 
that  such  a  restoration  of  the  pyramid  answers  to  the  Brit- 


*]6  Construction  of  the  Great  Pyramid.       §  38. 

ish  measures,  in  inches  and  feet,  of  that  structure,  then  it 
would  seem  almost  impossible  for  even  exacting  criticism 
to  charge  upon  such  a  complicated  series  of  correspondences 
the  escape  of  coincidence. 

(§  38.)  Professor  Piazzi  Smyth  has  given  to  the  world 
a  mass  of  measures  of  this  structure.  He  was  laboriously, 
and  even  painfully,  careful  in  their  taking,  on  a  measure  ad- 
justed to  the  British  standard  at  Edinburgh,  even  to  the  bal- 
ancing and  dwelling  upon  tenths  and  sovnQixmQs  htmdredths 
of  inches.  He  had  found  such  discrepancies  in  the  measures 
of  the  multitudes  of  those  who  had  preceded  him,  that  he 
was  prepared  beforehand  for  his  work.  Besides,  he  desired 
to  discover  who  of  those  others  had  done  their  work  well. 
Of  those  wlio  had  preceded  him,  he  found  the  measures 
of  Col.  Howard  Vyse,  of  the  French  savants,  and  of 
Professor  Greaves,  exact  and  reliable. 

(§  39.)  There  are  four  points  to  be  taken  into  considera- 
tion, and  which  should  always  be  had  in  mind  in  this  mat- 
ter, viz  : 

{a.)  That  it  is  next  to  impossible  to  have  measuring  in- 
struments alike,  though  taken  from  a  same  standard  ;  and 
it  is  almost  impossible  that,  even  though  having  the  same 
measures,  their  uses  will  bring  out  the  same  results.  Dis- 
crepancies are  liable,  from  these  causes,  to  show  them- 
selves in  tenths  of  inches,  and  even  more,  where  lengths 
of  thirty  or  more  feet  are  taken.  No  one  will  better  ap- 
preciate this  statement  than  Professor  Smyth. 

{b.)  Professor  Smyth  says  most  truly,  in  relation  to  the 
pyramid  structure  : 

"  The  differences  amongst  our  own  results  are  partly  due  to 
dilapidation  effects,  but  are  partly  dependent,  also,  on  variations 
introduced  by  the  builders,  or  actual  errors  in  their  work,  as  where 
the  breadth  of  the  grand  gallery  varies  in  different  parts  of  its  length 
irregularly,  anywhere  between  81.7  and  83.0  inches.  Another 
source  of  error  is  more  uncertain,  as  where  two  parts  taken  b}' 
Sir  Isaac  Newton,  and  most  other  writers,  as  certainly  intended 
to  be  the  same  in  measure,  are  found  to  be  positively  different. 
An  example  of  this  is  presented  in  the  breadth  and  height  of  the 
ramps,  assumed  by  Sir  Isaac  to  be  equal,  but  found  by  my  meas- 


§  40.       Construction  of  the  Great  Pyramid.  77 

ures  to  be  (on  the  mean  of  a  number  of  places,  but  nowhere  uni- 
formly) nearly  an  inch  different,  without  a  probable  uncertainty 
of  more  than  1  — 10  inches." 

(c.)  In  long  distances,  in  great  masses  of  mason-work,  it 
is  absolutely  impossible  to  practically  obey,  by  reason  of 
jointing,  the  mathematical  exactitudes  of  the  architect. 

id.)  Professor  Smyth  found  a  very  curious  feature  as  to 
lengths  of  passage-ways,  the  proportions  of  the  king's 
chamber,  and  of  the  coft'er  therein.  He  also  infers  the 
same  as  to  the  grand  outlines  of  the  pyramid  base.  It  is  : 
(i.)  That  a  passage-way  may  present  two  lengths,  the  east 
side,  say,  being  longer,  or  shorter,  than  the  west  side. 
(2.)  That,  compared  with  a  perfect  cubical  chamber,  the 
king's  (and  queen's)  chamber  is  out  of  shape,  or  askew. 
(3.)  The  same  happens  as  to  the  coffer.  Very  many  cir- 
cumstances connected  with  these  irregularities  of  admeas- 
urements would  seem  to  point  them  as  purposed,  so  that 
the  differences  between  the  measures  of  a  standard  cubical 
chamber,  or  coffer,  and  these  as  they  are,  served  to  give 
some  derived  result  as  the  working  out  of  a  problem ;  or 
else  that  a  purposed  variation  in  height  or  breadth  might 
be  intended  to  satisfy,  in  fact,  two  sets  of  measures  differ- 
ing from  each  other  by  some  very  slight  quantity. 


SECTION   II. 

STANDARD  MEASURES  OF  THE  PYRAMID.  ENLARGEMENT  ON  THE 
SAME,  WITH  THE  REASONS  WHY.  THE  STANDARD  AND  EX- 
ACT, OR  ENLARGED,  MEASURES  OF  THE  KING'S  CHAMBER. 

Standard  Afeasures  of  the  Pyramid. 

(§40.)  As  to  the  objects  of  construction  of  the  great 
pyramid  of  Egypt :  {a.)  One  may  be  taken  as  astronomi- 
cal, from  the  facts,  that  the  north  base  side  of  the  structure 
coincides  with  the  parallel  of  30°  north  latitude,  and  that 
the  mass,  as  to  its  sides,  evidenced  by  its  corner  socket 


78  Construction  of  the  Great  Pyramid.      §41. 


lines,  is  oriented  as  perfectly  as  could  be  expected  of 
human  ability,  (d.)  Another  may  be  taken  as  geometrical. 
It  was  considered  by  the  Rev.  Mr.  Taylor,  who  had  made 
this  structure  a  study  (see  "  Our  Inheritance  in  the  Great 
Pyramid,"  by  P.  Smyth,  prior  to  his  "  Life  and  Works"),  that 
it  was  so  built  that  its  height  should  be  to  one-half  its  cir- 
cumference as  diameter  to  circumference  of  a  circle.  Pro- 
fessor Smyth  shows  that  approximately  this  was  the  fact. 
Upon  carefully  taken  measures,  linear  and  angular,  and 
upon  computation,  he  comes  to  the  result  that  the  structure 
was — 

In  height,  486  feet,  2  inches  ; 

And  that  its  base  side  was,  by  the 
measures  of  Col.  Howard  Vyse,  in 
length,  764  feet; 

And,  by  the  measures  of  the  French 

62 
Corfs.  763  feet. 

(§  41.)^  Take,  as  the  result  of  Mr.  Parker's  problem  of 
three  revolving  bodies,  his  formula  for  obtaining  the  sun's 
time,  or  rather  the  time  of  the  earth  about  the  sun.     It  is — 

4*4 
(i.)     20612  X  -=27482.66+,  and  this  X  -  =  36643.55+; 

in  which  the  last  term,  being  the  direct  product  from  20612, 
or  value  of  circumference,  pointed  at  '^66,  is,  as  Mr.  Par- 
ker says,  "  the  exact  value  of  the  passage  of  the  earth 
around  the  sun,  over  one  complete  circle  in  space,  in  cir- 
cular days."    The  diameters  to  correspond  with  this  formula 

are — 

4  4 

(2.)     6561  X  -  =  8748,  and  this  X  -=  11664. 

Let  it  be  remembered  that,  though  this  formula  is  taking 
the  part  of  time  values,  it  nevertheless  is  also  in  the  value 
of  British  inches. 

Take  the  two  results  and  divide  them  by  12,  thus  reduc- 
ing them  to  feet — 

(3.)     11664  ^  C  972  feet  for  diameter. 

>  -^  12  =  ^  [ence. 

36643.55+  )  (  3053-629+  feet  for  circumfer 


§  4i«    Standard  Measures  of  the  Same.      79 

Then  972  -f-  2  will  give  the  height  as  radius,  and  3053.629-f- 
wiil  be  the  circumference  of  base  equal  to  the  circumfer- 
ence of  a  circle  to  a  radius  of  that  height ;  or  486  will  be 
the    diameter   value    to   twice    the    side    of    base,    or    to 

3053.629 

—  =  763.407  X  2  =  1526. 8144-  feet,  taken  as    cir- 

4 
cumference  of  a  circle.     These  are  the  proportions  corre- 
sponding to  those  of  the  great  pyramid. 
This  division  gives — 

(4.)     For  height,        486  feet. 

407-}- 
For  base  side,  763. feet. 

Compare  these  with  Professor  Smyth's  results  in  British 

values,  viz  : 

(5.)     For  height,  486  feet,  2  inches. 

62 
For  base  side  (French  measure),  763. feet. 

Hence,  the  great  pyramid  exhibits  itself  as  one  not  only 
monumenting  a  method  of  quadrature,  the  elements  of 
which  we  possess,  but  also  a  measure  of  the  sun^s  time,  and 
also  the  British  inch  and  foot  values.  On  the  premises 
and  conclusion,  then,  the  Parker  elements  seem,  by  a  very 
strong  showing,  to  have  been  known  and  used  in  the  build- 
ing of  this  structure.  The  worth  of  having  a  unit  of  meas- 
ure, common  for  the  expression  of  different  kinds  of  value, 
is  also  apparent ;  for  here  astronomical  and  geometrical 
values  are,  by  means  of  the  common  mason's  measure  in 
inches  and  feet,  built  into  a  stone  book.  It  is  thought  that 
the  idea  is  practically  carried  out  in  details,  passing  from 
more  generalized  to  and  through  complex  calculations ; 
evidenced  by  the  chamber,  coffer,  and  other  fine  work  of 
the  interior.  Even  color  may  be  used  to  classify  or  qualify 
the  kinds  of  measure  intended. 

The  formula  in  (3),  viz  : 

11664  ^  (  972 

36643.54-  S  X  3053-629 

is  the  same  as — 


8o  Construction  of  the  Great  Pyramid.      §42. 


(6.)     6561  >        x6        (   , 

V  X  —  =  \  t"6  same  ; 
20612  )       ^08       I 

where  use  is  made  of  the  origiricil  Parker  elements.  . 

It  may  be  taken,  then,  as  determined,  that  this  pyramid 
structure  was  planned  in  the  measure  of  reductions  irom 
the  Parker  elements,  and  that  they  are  the  standard  meas- 
ures employed  in  its  entire  building,  whether  in  mass  or 
detail,  subject  to  variatiofis  on  these  standards,  in  the 
working  out  of  the  various  problems  contained  in  the  whole, 
and  various  parts. 

Standard  Measures  of  the  King's  Chamber. 

(§42.)  Take,  as  one  set  of  derivations  in  detail,  the 
dimensions  of  the  King's  chamber — 

(i.)     206.12  inches  -^  12  =  10  cubits,  or  17.1766+  feet. 
(2.)     17.1766+  feet  X  2  =  20  cubits,  or  34.3533+  feet. 

17280 
(3.)     20612  -4-   -^,  or 

\  =  1Q.08S1+  feet ; 
10  I  y       ^ 

34-3533  X  ^ 

which  measures,  agreeably  to  the  conditions,  are  the  meas- 
ures, taken  at  the  standard,  of  the  King's  chamber;  (i)  or 
17.1766+,  being  standard  breadth,  (2)  or  34-3533  +  ,  being 
standard  length,  and  (3)  or  19.0851  +  ,  being  the  standard 
height,  all  in  British  feet ;  subject  to  variations  therefrom 
for  special  purposes,  as  will  be  shown.  The  measures  of 
this  chamber,  as  given  by  Professor  Smyth,  are — 

Breadih,  i7-i9  feet, 

Length,  34.38     " 

Height,  from       19.  i  > 

to  19.179  feet.  > 
(As  to  height.  Professor  Smyth  gives  his  measures  19. i  to 
19.179,  with  allowance,  or  as  conjectural,  because  of  the 
broken  state  of  the  floor  when  he  took  them.  '■^  Floor 
broken  up  thus  since  the  measures  of  Col.  Howard  Vysc.^' 
His  measure  for  height  was  19. i  feet.) 


§  44*  Measures  by  Enlargement  on  Standard.   8i 

Actual  Pyramid  Measures,  as  Enlargements  on  the  Stand- 
ard, with  the  Reason  for  the  Variation. 

(§  43.)  The  following  is  a  method  of  variation  on  the 
standard  measures  as  given  ;  and  one  which  seemingly 
controls  the  entire  pyramid  structure.  The  Parker  ele- 
ments are  20612  to  6561.  The  cubit  value  is  20.612  -f-  12 
=  1.71766+  feet;  and  10  cubits  are  17.1766+ feet.  If  the 
value  of  diameter  6561  taken  as  feet,  be  divided  by 
17.1766+,  or  the  measure  of  10  cubits,  thus  derived,  the 
quotient  will  be  381.97166+  feet.  This  method  is  given 
for  its  results  in  the  actual  measure  desired. 

This,  in  effect,  is  the  same  as  the  division,  or  quotient,  of 
diameter  value  of  6561  by  circumference  value,  or  20612, 
under  a  formulation  to  obtain  a  diameter  value  to  a  circum- 
ference of  unity,  thus  : 

(i.)  20612  :  6561     :  :     i  :   .3183097  +  ,  and, 

(2.)  31.83097x12  =  381.97166+, 

and  this  X  2  =  763.94333. 

The  effect  is  a  very  curious  one.     Take  the  following : 

(3.)  20612  X^=  36643.55-^-48  =763.407+, 

where  the  standard  base  side  is  obtained  from  the  primary 
circumference  value.  By  (i.),  3183097  is  3. diameter  Ydlue, 
and  raising  it  as  shown,  it  becomes  763.94333,  being  al- 
most the  same  by  comparison.  Then,  working  in  circum- 
ference values,  the  standard  pyramid  measures  are  found  ; 
working  in  diameter  values,  the  exactitude  comes  by  the 
enlarganent.     Referred  to  a  primary  principle. 

Original  circumference  \Si  20612. 

Changing  to  diameter  value,  it  becomes  20626.47001 +  . 

(§  44.)     The  standard  measure  of  the  side  of  the  pyra- 
mid in  (§  41)  (4),  was  763.4074+  feet.     The  half  of  this 
is  381.7037+  feet.     Compare  this  value  with  that  obtained 
by  the  method  of  variation  shown  in  (§  43) ; 
(i.)     Standard^     381.7037  + 
Variation,    381.9716  +  . 
This  last  multiplied  by  2  =  763.94333+  feet  for  the  side  of 


82  Construction  of  the  Great  Pyramid.      §46. 

base  of  pyramid,  instead  of  763.4074+  feet;  and  let  it  be 
assumed  that  this  was,  in  fact,  a  variation  taken  on  the 
standard  measure,  yet  one  growing  out  of  the  Parker  ele- 
ments. 

Taking  the  base  side  at  763.94333+  feet,  the  proportion- 
ate height  of  the  mass  would  be, 

(2.)     486.341+  feet, 
instead  of  486  feet  as  by  the  standard. 

(§  45.)     This  measure  of  the  pyramid's  base  agrees  with 
that  taken  by  Col.  Howard  Vyse,  as  follows  : 
Vyse,  764.000      feet, 

Above,  763-943+ »    " 

Difference,  .056+,    " 

or,  to  within  less  than  one  inch  in  9168  inches. 

This    Variation    of  Enlargement  A^^lied  to   Ascertain 
the  Measures  of  the  King's  Chamber. 

(§  46.)  If  this  variation  on  the  standard  be  applied,  for 
the  admeasurements  of  the  king's  chamber,  to  ascertain 
the  enlargements  on  the  standard,  there  will  result,  as  a 
base  of  estimate  (§  43),  206.2647001+  as  the  enlargement 
on  the  Parker  circumference  of  206.12  ;  and, 

(i.)     206.2647-^12  =  17.1887+ 
as  the  enlarged  width  of  the  king's  chamber ; 

(2.)     17.1887  X  2  =  34.37745  + 
as  the  enlarged  length  of  same  ;  and, 

(3.)     34-3774  X  ^g  =  19.0985  +  , 

as  the  enlarged  height  of  same. 

Or,  comparing  these  with  the  aetual  measures  taken 
(§  42),  as  above,  there  results  : 

(4.)     Actual  measured  breadth,  17-19  feet. 

As  above,  17.1887    ♦' 

Difference,  — ^  of  a  foot,       .0013    '* 
1 0000 


§  47     Measures  by  Enlargement  on  Standard.        S^ 

(5.)     Actual  measured  length,       34-38  feet. 
As  above,  34-3774   " 

26 

DifFerence of  a  foot,  .0026    " 

1 0000 


(6.)     Actual  measured  height,        19.100      feet. 
As  above,  19.09854-      " 

Difference,  ^  of  a  foot,    .0015         " 

1 0000 

or,  literall}^  the  difference  has  become  so  inappreciable 
that  there  is  no  method  of  ascertainment  as  to  what  the  cor-  ,  J-  qjJ 
rect  admeasurement  is,  by  any  practicable  test  of  actual 
measure.  //,  hozucver,  a  lazv  can  be  ascertained,  which 
will  in  its  fulfillment  demand  the  use  of  these  variations  on 
the  standard,  then  thev  should  be  considered  as  data  cor- 
rectly  taken.  There  is  such  a  laiv ;  and  its  demands  as  to 
their  nature  coincide  with  the  spirit  or  genius  of  the  pyra- 
mid structure,  as  a  measure  of  time. 

Eminciation  of  the  Law. 

(§  47.)  The  very  great  value  of  the  number  6  as  a  fac- 
tor, is  at  once  recognized  in  the  base  of  the  British  long 
and  land  measures,  and  also  in  the  construction  of  the 
celestial  time  circle.  That  circle  is  of  the  value  of  360° ; 
it  is  divided  into  minutes,  seconds,  thirds,  etc.,  in  the  scale 
of  60'=  1°,  60"  =  i',  60'"=  i",  and  so  on.  This  circle  is 
subject  to  another  division,  as  applied  geographically  to  the 
earth,  where  36o°-^24  =  i5°  to  the  hour  of  longitude, 
where  24  is  also  a  multiple  of  6,  as  6  X  4  —  24,  and  where 
each  degree  =  69+  miles  British.  The  primary  division 
of  this  circle  is  on  the  base  of  6  parts,  subdivided  for  each 
part  into  3600  parts,  or  6  X  3600  =  21600' ;  or,  360°  x  60' 
==21600'. 

Now,  by  the  variation  on  the  Parker  elements  (stand- 
ard), worked  out,  as  seen,  through  the  simple  use  of  the 
elements  themselves,  the  result  is  obtained  of  a  diam- 
eter value,  (by  change  on  a  circumference  value),  of 
1909854-  [§  46,  (3)]. 


84  Construction  of  the  Great  Pyramid.       §  47 

This  factor  6,  which  is  of  such  great  value,  is  not  taken 
empirically ,  merely  because  it  proves  to  be  of  such  great 
practical  use  in  the  admeasurement  and  subdivision  of  time 
periods  or  land  measuring  rests,  or  stops,  hut  it  is  a  legiti- 
mate circumference  value,  derivable  from  this  variation 
on  the  standard  Parker  elements  of  diameter  and  circum- 
ference, for — 

(i.)     6561    :    20612    ::   381.97166   :    1200   ::    190.985  + 

:    600   :  :    1.90985    :    6 ; 

6561 
where     the     reduction     from      ^      =  3183094-  X  12  = 

38197166,  or  —      ..  =  381.97166,  divided  by  2  =  190.985, 

becomes  the  diameter  value  of  a  circumference  of  600;  or, 
1.90985  becomes  the  diameter  value  of  a  circumference  of 
6 ;  and  this  properly,  and  rightly,  and  exactly,  belongs  to 
jthe  use  of  the  Parker  elements  :  so,  this  height  of  the 
kinc's  chamber  is  diameter  to  a  circumference  of  60.  See 
the  play  of  change!  The  Parker  circumference  20612, 
changed  to  a  diameter  value  by  variation,  gave  the  exacti- 
tudes of  measure  of  the  pyramid  in  diameter  for  circum- 
ference terms.  Among  these  is  the  height  of  the  king's 
chamber,  which  now  turns  out  to  be  a  means  of  re-getting 
an  integral  circumference  value,  in  the  number  6,  or  60. 
The  obtaining  of  this  end  scans  to  be  the  law  of  pyramid 
actual  construction. 

216         6^  ,    .     r 

(2.)  19.0985+  mches  X  —  ,  or  — ,  =  ^12. $2g^-\- inches, 

which  equals  the  length  of  the  king's  chamber  in  inches, 
as  the  enlargement  or  variation  on  the  standard ;  and, 

(3.)  6561  :  20612  ::  412.5294+  :  1296; 
or,  there  results,  the  length  of  the  king's  chamber,  in  in- 
ches, as  a  diameter  value,  proportioned  to  the  number 
of  inches  in  the  square  yard  British,  as  a  circumference; 
and  it  is  well  to  reflect  that  1296  X  4  =  5184,  the  charac- 
teristic value  of  one  solar  day  reduced  to  thirds. 

4i2t;Q.24 :  120600       ^  ^ 

(4.)  \ =  6875.48+  :   21600, 


§  48-  Law  of  Enlargement  on  the  Standard.   85 

and, 

6875.48  :  21600 
(5-)  360  =  19-0985  '  60; 

where  the  celestial,  or  geographical  earth,  circle  of  (6  X 
60,  or)  360°  X  60',  equals  21600'  of  division,  in  terms   for 
circumference  to  height  of  the  king's  chamber  as  diameter. 
This,   as   a  foundation,  embraces  all  the  time  subdivisions 
of  that    circle    into    hours    (24    equal    to    i    solar  day   of 

/i44\ ^ 

(—  j  X  1000  =  5184000'",  as  well  as  the  distance  divis- 
ions of  the  circumference  of  the  earth  in  miles  to  the  de- 
gree), minutes,  ov  p7-i)]ics,  seconds,  and  thirds. 

So,  also,  as  to  the  width  of  the  king's  chamber. 

(6.)     6561  :   20612     :  :     206. 264 -f  inches  :  648  inches. 

So  the  law  of  construction  of  the  pyramid  is  assumed  to 
have  been  found  on  this  showing. 

Note,  that  the  base  side  of  the  pyramid,  by  actual  measure, 
being  thus  shown  to  be  a  diameter  of  763.943-}-  to  a  circumfer- 
ence of  2400  feet,  this  is  24  X  100,  and  34  is  four  times  the  fac- 
tor 6.  The  base  of  the  pyramid,  then,  would  be  co-ordinately 
represented  b}'  a  square  of  24,  or.  6X4=  24,  to  the  side  ;  and 
this  is  the  Garden  of  Eden  form  :  and,  also,  it  is  the  square 
Hebrew  Zodiac  of  the  12  months. 

The  Discovery  of  this  Law. 

(§  48.)  The  discovery  of  this  law,  and  of  its  applica_ 
tion,  arose  from  a  suggestion  of  thought  on  reading  a  pas- 
sage in  the  '■'■Historical  View  of  the  Hindu  Astronomy  ,^''  by 
Mr.  John  Bentley.  It  is  almost  evident  that  one  intention 
of  the  architect  of  the  pyramid,  has  been  exactly  repro- 
duced in  the  use  of  a  numerical  system  ;  and  this  accom- 
plishment is  but  the  going  back  to  the  original  sources  of 
the  numerical  instrumentalities  which  are  in  use  to-day. 
Considering  the  value  of  this  discovery,  it  is  appropriate  to 
give  the  original  notes  made  on  the  subject,  as  follows 
( premising,  however,  that  the  author  had  before  this  obtained 
the  numerical  value  of  the  enlargement  on  the  standard, 


86  Construction  of  the  Great  Pyramid.       §  48 

and  had  made  use  and  mention  of  it  in  Ancient  of  Days, 
without  knowing,  or  seeing  its  application)  : 

"A  very  remarkable  blending  of  all  these  systems  can  be 
given,  arising  from  the  actual  method  used  by  the  Hindus, 
for  the  calculations  of  sines,  tangents,  cosines,  cotangents, 
etc.,  which  belongs  to  their  most  ancientsystem  of  astronomi- 
cal calculations.  This  method  is  given  by  Mr.  John  Bent- 
ley,  in  his  '■'' Historical  View  of  the  Hindti  Astronomy" 
(sec.  3,  page  156).  He  is  giving  the  various  values  for 
the  computations  of  the  value  of  tt,  one  after  the  other, 
until  coming  to  one  very  nearly  approximating  the  true  re- 
lation, he  says  : 

"  But  Argabhatta,  in  the  17th  chapter,  in  speaking  of  the  orbits 
of  the  planets,  gives  us  a  nearer  approach  to  the  truth  ;  for  he 
there  states  the  proportion  as  191  to  600,  or  as  i  :  3.14136,  which 
gives  the  circumference  a  small  matter  less  than  the  proportion  of 
Bhaskara  in  the  Lilavati.  This,  however,  is  not  the  invention  of 
Argabhatta  ;  for  it  is  employed  in  the  Brahma  Siddhanta,  Surga 
Siddhanta,  and  by  all  the  astronomers  before  the  time  of  Arga- 
bhatta, as  well  as  since,  for  computing  the  tables  of  sines,  etc., 
though  not  immediately  apparent.  Thus,  in  computing  the  sines, 
they  take  the  i^adius  at  3438',  and  the  circumference  they  divide 
into  21600' ;  the  diameter  is  therefore  6S76 :  hence  the  proportion 
is  6S76  :  21600.  Reduce  these  numbers  to  their  last  terms  by  divid- 
ing them  by  36,  the  result  will  be  191  :  600,  as  stated  by  Arga- 
bhatta." 

"Mr.  Bentley  was  greatly  familiar  with  the  Hindu  astro- 
nomical and  mathematical  knowledge  ;  not  as  a  foreigner 
studving  the  reach  of  a  nation  in  such  matters,  but  as  a 
resident  in  Hindostan  of  some  fifty  years.  This  statement 
of  his  may,  then,  be  taken  as  authentic.  The  same  re- 
markable trait,  among  so  many  Eastern  and  ancient  nations, 
of  sedulousl}^  concealing  the  arcana  of  this  kind  of  knowl- 
edge, is  a  marked  one  among  the  Hindus.  That  which 
was  given  out  to  be  popularly  taught,  and  to  be  exposed  to 
popular  inspection,  was  but  the  approximate  of  a  more  ex- 
act but  hidden  knowledge.  And  this  very  formulation  of 
Mr.  Bentley  will  strangely  exemplify  the  assertion  ;  and, 
explained,  will  show  that  it  was  derived  from  a  system  ex- 
act beyond  the  European  one,  in  which  Mr.  Bentley  him- 


§  48-  Law  of  Enlargement  on  the  Standard.    87 

self,  of  course,  trusted,  as  far  in  advance  of  the  Hindu 
knowledge,  at  any  time,  in  any  generation. 

"  Tliis  formulation  is  the  taking  of  a  radius  of  3438  to 
obtain  a  circumference  to  be  divided  into  21600  equal  parts. 
The  diameter  would  be  6876,  and  the  reduction  of  this  by 
36  would  be  191.  216  is  6^,  or,  36  X  6,  which  shows  use 
of  a  system  founded  on  a  multiple  of  which  6  is  the  basic 
factor.  3438  is  an  exceedingly  near  approach  to  a  pure 
circumference  value ;  which  goes  to  show,  as  it  is  used  as 
a  radius,  that  which  has  been  so  observable  heretofore  of 
the  expression  of  diameter,  or  straight  line,  values  in  terms 
of  circumference. 

"Take  the  reductions  of  20612,  the  Parker  circumfer- 
ence value,  that  give  the  dimensions  of  the  king's  cham- 
ber : 

(i.)  20612  -4-    600  —  34.3533+  feet,  =  standard  length. 
(2.)  20612 -^  1200  —  17.1766-}- feet,  =        *'         width. 

20612  -;-  1080  \ 
(3-)  343-533  -^      18  V=  19.0851+  feet,  =  standard  height. 
190.851  -f-      10  ) 

"  These  are  the  standard  measures  of  these  dimensions, 
for  comparison  ;  or,  on  which  variations  are  raised  in  the 
working  out  of  the  various  problems  for  which  they  were 
the  base.  Take  it  that  this  Hindu  problem  involves  these 
measures,  and  that  the  system  of  factoring  by  6  is  intro- 
duced, by  which  with  these  measures  to  work  out  tables  of 
sines,  cosines,  tangents,  cotangents,  etc.,  and  for  calcula- 
tions oi  ^planetary  times,  or  distances.  So  (i),  perfect  cir- 
cular elements  are  required  ;  and  (2),  the  circumference  of 
these  elements  is  to  be  divided  into  21600  equal  parts.  Can 
not  the  Hindu  system  be  traced  back  to  an  absolutely  per- 
fect,one,  based  on  the  Parker  elements?  And,  at  the  same 
time,  can  not  this  same  Hindu  S3'stem  be  attached  through 
the  same  Parker  elements,  by  actual  measures,  to  the 
king's  chamber,  the  passage-way  therefrom,  and  to  the 
ante-chamber  works?  If  this  can  be  done,  plainly,  and 
mathematically,  it  will  be  an  important  achievement. 

"Let    use    of    the    base   of    operations    be    in   whole 


88  Construction  of  the  Great  Pyramid.      §  48. 

numbers,    viz.,     20612,    the    perfect    circumference,    in- 
stead of  its  fractional  derivatives.     A  perfect   radius,  in- 
stead of  being,  as  Mr.  Bentley  represents  that  of  the  Hin- 
dus, or  3438. 
is,  say,  the  perfect  one  of  3435-333+ 
or,  2061200-^600.     The  diameter,  then,  in- 
stead of  being  6876,  will  be  6870. 66-|- 
or  4122400  -^  600. 

"Let  Mr.  Bentley 's  Hindu  radius  values  be  tested  with 
the  perfect  ones — 

(4.)  19.0851  :  34-3533+  '■  1910  •  3438-oi5  5 
where  standard  height  of  the  king's  chamber  is  to  its  stan- 
dard length  as  Mr.  Bentley's  diameter  reduction  is  to  the 
diameter  value  he  reduces  from,  3438,  plus  the  increment, 
to  make  up  the  exactitude,  of  .015,  as  seen.  Comparison 
with  the  standard  values  of  king's  chamber  measurement 
is  thus  made,  subject  to  variations  on  these  for  special  pur- 
poses. Howard  Vyse's  height  of  the  king's  chamber  z's 
19. 1,  and  Professor  Smyth's  measured  length  of  the  same 
z's  34.38,  the  very  numbers  of  Mr.  Bentley. 

"  It  is  now  desired  to  get  a  perfect  circumference  to  di- 
vide into  21600  equal  parts,  and  for  trial — 

(5.)     6561    :    20612    : :    41224   :    129509. 0821  ; 
that  is,  diameter   :    circumference   :  :    standard   length  of 
king's  chamber  in  one-hundredths  of  inches  :    circumfer- 
ence required.     Divide  this  fourth  term  by  21600,  to  see 
what  the  value  of  the  subdivided  parts  will  be — 
(6.)     129509.0821-^21600  =  5.995790; 
and  here,  in  this  result,  is  evidently  to  be  seen  one  object 
of  the  Hindu  system,  as  to  the  values  taken  to  get  this  di- 
vision, viz.,  io  create  a  system  from  a  numerical  base  0/6, 
which  may  be  used  as  a  factor  throughout  the  system  de- 
veloped. 

"  21600  is  the  cube  of  6,  or  6^  X  100,  and  here,  in  the 
quotient,  by  the  division  of  21600  into  the  circumference  value 
taken,  there  is  obtained  5.99+,  or  a  result  with  an  exceed- 
ingly near  approach  to  the  factor  6,  desired  as  the  base  of 
the  system.     But  this  base  is  wanted  exactly ;    therefore, 


§  48.   Law  of  Enlargement  on  the  Standard.    89 

force  back  a  perfect  circumference  value  into  an  enlarged 
form,  to  accommodate  to  this  state.  Were  this  quotient  6, 
instead  of  5.99+5  the  dividend  would  be  1296  (by  the  way, 
the  number  of  square  inches  in  the  square  yard),  instead 
of  1295  +  .  Carry  back,  then,  with  this  value,  by  the  pro- 
portion from  the  standard  of  Parker  circular  elements,  and 
there  results — 

(7.)      20612   :    6561    ::    129600   :    41252.94-}-, 
for   the    desired    diameter   value    in    the    fourth    term,  in 
hundredths  of  inches,  as  an  enlargement  upon  the  standard 
length  of  the  king's  chamber  measure.     Compare  this  with 
the  standard — 

(8.)  Enlarged  value,  41252.94 

Standard     "  41224 

Difference  in  hundredths  of  an  inch,         28.94, 
as  a  variation  on  the  standard  to  obtain  the  desired  result. 

(9.)  41252.94-^12  =  3437.74  + 
is  the  radius  required  to  complete  the  object  sought ;  or, 
the  diameter  will  be — 

(IO-)  3437-74  X  2  =  6875.48. 
"  x^nd  this  is  taken  to  be  the  real  radius,  and  the  real 
diameter  belonging  to  the  Hindu  system  ;    which  was  just 
sufficiently  obscured  to  cover  the  real  derivation  from  the 
perfect  elements  of  the  quadrature. 

(11.)  The  radius  given  by  Mr.  Bentley,  is        3438.00 

The  true  one  is  3437-74 

The  diameter  given  by  Mr.  Bentley,  is  6876.00 

The  true  one  is  6875.48 

And  again  : 

^      ^  6875.48  :  2i6oo     .  r.  ^ 

(12.)  -> gives  190.985+  :  600, 

for,  and  in  place  of  Mr.  Bentley's   Hindu  proportion  of 
191  :  600. 

"  Now,  applying  these  results  as  a  variation  on  the  height 
and  length  of  the  king's  chamber,  the  standard  measures 
are,  respectively  : 

(13.)  19.0851+  :  Z^.Z^Zl-^' 


90  Construction  of  the  Great  Pyramid.       §  48. 

The  variations  for  the  purpose  stated,  give  : 
(14.)   19.0985+  :  34-3774+5 
while  the  actual  measures  made,  are  : 

(15.)  19. 1  :  34.38; 
and  in  mason  work  of  these  lengths,  the  difference  between 
19.0985-I-  and  19. 1,  and  between  34.3774+  and  34.38,  in 
feet,  is  certainly  inappreciable.  While  this  is  so,  the  pur- 
pose of  the  Hindu  use  is  also  thus  shown  to  be  perfectly 
fitting  in  measures,  to  such  a  use  in  the  pyramid  ;  and  the 
pyramid  work,  just  here,  almost  undoubtedly  involves  cir- 
cular admeasurements. 

"  This  slight  but  proportionate  change  is  made  to  give 
a  circumference  value  into  which  21600,  as  6^  X  100,  will 
divide  evenly  into  subdivision  of  6.  And  thus,  and  here, 
and  in  this  manner,  is  shown  the  working-in  of  the  system 
of  the  division  of  a  circle  into  360  equal  parts,  and  further 
subdivisions,  to  co-operate,  and  to  co-ordinate,  with  pure 
circular  measure.  21600  -^  60  =  360,  or  360°  of  60'  to  the 
degree.  360°  -^-  24  hours  =  15°  to  the  hour.  If  the  min- 
utes in  24  hours  are  taken,  or  24  X  60'  =  1440',  then  1440 
-^2  =  720',  and  720'^  =1518400',  and  this  X  10=  numer- 
ically, and  in  minutes^  just  one  solar  day  in  its  last  subdi- 
vision of  thirds;  and  in  the  limits  of  144  and  5184,  are 
to  be  found  the  peculiar  limits  of  the  British  square  foot, 
and  four  times  the  British  square  yard  of  1296  inches  :  and 
the  British  acre  is  the  only  least  quantity  into  which  5184 
will  divide  without  a  remainder.  5184  is  again  repro- 
duced by  81  X  64,  where  the  81  is  the  square  root  of  the 
Parker  square  of  6561,  and  the  64  is  one-tenth  the  number 
of  acres  in  the  square  mile. 

"  So,  an  exceedingly  practical  use  is  thus  developed,  as 
belonging  to  the  meanings,  or  readings,  of  the  king's 
chamber." 


§  50.  Factor  6  in  the  Metius  Form.  91 

NOTE. 

A  Connection  between  the  Parker  and  Metius  Forins  with 
Relation  to  the  Factor  6. 

(§  49.)     In  §  35  (3),  it  is  seen  that  we  have  the  forms : 
(i.)     6561    :   20612     :     113  :  "355.0001  +  , 
and — 

(2.)  113  :  35500014-  ::  36  :  II3-09734-. 
Above,  we  have  the  change  of  circumference  to  diameter 
values,  to  obtain  the  exact  measures  of  the  pyramid,  with 
dimensions  of  the  king's  chamber,  of  which  height  of 
king's  chamber  is  a  base  of  change,  again,  from  a  diam- 
eter, to  get  a  circumference  value,  viz.,  in  the  form — 

(3.)     1.90985+   :    6; 
where  the  third  proportional  is  diameter  to,  the  fourth,  a 
circumference  of  6. 

Through  a  like  change  on  the  Metius  forms,  we  find  in 
the  third  proportional  of  (2)  6^,  or  6  X  6,  or  use  of  6  as 
a  factor,  for  a  diameter  value,  to  the  fourth,  that  of  a  cir- 
cumference. 

Both  forms  thus  find  a  like  base  of  structure  on  the  same 
factor,  6 ;  but  one  finding  it  as  circumference,  and  one 
as  diameter  value.  It  is  thought  that  herein,  perhaps, 
is  a  key  to  one  of  the  chief  links  of  connection  between 
the  two  forms. 


SECTION  II. 

TABLE  OF  standard  MEASURES  OF  RESTORATION  OF  THE  GREAT 
PYRAMID,    MADE    THUS    FAR. 

(§  50^)    Standard  circumference  in  inches,  20612.00 
For  circumference  of  base,  raised  to  36643.55 

Standard  diameter  in  inches,  6561.00 

1 1 664 
For  height  of  pyramid,  raised  to  -^ — .00 

Standard  circumference  of  pyramid, 

36643.55+  -^  12  =  in  feet,  3053-62  + 

in  cubits,  1777-77  + 


92 


Construction  of  the  Great  Pyramid.       §  51. 


Standard  base  side  of  pyramid, 

3053.62+  -r-  4  —  in  feet, 

763.4074 

in  cubits, 

444.444 

in  inches, 

9160.88 

Standard  height  of  pyramid. 

11664    :    24  —  in  feet. 

486.00 

Standard  length  of  king's  chamber. 

206.12  X  2  =  in  inches, 

412.24 

in  feet. 

34-3533 

in  cubits, 

20.0000 

Standard  breadth  of  same. 

in  inches, 

206.12 

in  feet, 

17.1766-f- 

in  cubits, 

10.000 

Standard  height  of  same, 

Base  side,  763.4074  -^  40,  \ 

ii.iiii/  in  feet, 

19.08518 

or,  20.012  A                  V 

10         \  in  inches, 

229.0222 

or,  34-3533  X  18        / 

in  cubits. 

II. mil 

Enlarged  Measures  on  the  Standard. 

(§  51.)  These  are  obtained  on  the  formula — 
6561  :  20612  ::  .318309+  :  i, 
where  the  object  evidently  is,  among  other  things,  to  get  a 
new  diameter  value  for  an  integral  circumference  value  of 
unity.  It  will  be  seen  that  this  new  diameter  value  can  be 
raised  so  as  to  exhibit  a  very  slight  enlargement  on  the 
standard  circumference  values  already  used. 
Enlarged  height  of  pyramid  in  feet. 
Enlarged  base  side,  ^ 

31.830972  X  24,    5   ~ 
And  this  is  a  dia.  to  a  circumference  of     2400.0000 
in  inches,  9167.31  + 


486.34118 
763-9433  + 


§53- 


Table  of  Measures. 


93 


Enlarged  height  of  king's  chamber, 

763-943328  --  40  ^  in  feet, 

in  inches. 

Enlarged  length  of  king's  chamber, 

18 
19.098583+  X  — =  in  feet, 

in  inches. 
Enlarged  width  of  same, 

34-3774497^  ^  2  =  in  feet, 

in  inches, 


19.098583 
229.182998 

34-37744976  + 
412.529396  + 

17.1887248  + 
206.2647001  + 


Measures  as  actually  Made  or  Comfuted  in  Terms  of  the 
British  Inch  and  Foot. 

(§  52.)     Height    (estimated    or    computed 

by  Smyth),  in  feet,  486.2  inches. 

62 
Side  of  base  (French  measures),  in  feet,  ^61. 

Side  of  base  (Col.  Vyse's  measures),  in  feet,  764.00 
Length  of  king's  chamber,  in  feet,  34-38 

Width        "  *'  "  17.19 

Height      "  "  '«  19.1 


(§  53.)  A  table  can  be  raised  on  these  enlarged  values, 
where,  in  every  case,  318+  is  the  quotient  of  the  diameter 
divided  by  the  circumference.  It  is  thought  that  the  use- 
fulness of  this  value  of  318+  is  just  that  which  gave  it  the 
name  of  the  318  trained  or  circumcised  servants  of  Abram. 


(a.)       1.9098+ feet  diameter  to  a  circumference  of      6  feet. 

3.8197+        "  "  "        12  " 

229.1829  inches  "  "      720  in. 

458.3658      *'  "  "    1440 


(( 


94  Construction  of  the  Great  Pyramid.       §  54. 

{p.)     34.377449  ft.  diameter  to  a  circumference  of  108  feet. 
412.529      inches  *'  *'    1296   in. 

103.132-I-      *'  "  "      324    " 

{c.)     68.754899  feet  <*  "      216  feet. 

825.058  inclies  "  "    2592    in. 

{d.)  137.509796  feet  "  "      432  feet. 

1650. 116+  inches  *'  *'    5184   in. 

{c.)    275.019592  feet  **  •'      864  feet. 

3300.232  inches  **  *'  10368    in. 

In  this  table,  it  is  seen  that  the  actual  pyramid  measures, 
for  one  feature,  become  diameter  values  for  circumferences 
of  which  6  is  a  factor.  This  is  a  fact  of  interest,  when  it 
is  considered  that  the  British  long  and  land  measures  are 
based  on  the  use  of  this  factor ;  so,  also,  the  Hebrew  ca- 
pacity measures ;  likewise,  also,  the  Hindu  measures  of 
time. 
The  characteristic,  or  value,  number  of  the  Hindu 

time  measures,  as  to  one  of  their  cycles,  is  108 

This  is  the  half  of  216 

That  of  another  period,  called  Kalpa,  is  432 

«'  "  "       Dwaper,  is  864 

"  <«  "        Sandhi,  is  1728 

That  of  one  of  their  divisions  of  months  is  5184 

It  is  thus  seen  that  the  factor  6  co-ordinates  long  and 
land,  and  capacity  and  time  measures,  belonging,  respect- 
ively, to  different  peoples. 

(§  54.)  There  is  also  a  system  of  factoring  to  obtain  the 
standard  pyramid  measures  from  the  value  of  a  circum- 
ference alone,  as  follows  : 

20612  X  -  =  27482.66-1-    Whence  the  lunar  time  by  Parker. 

^-=36643.55+         "         "    solar     "      "       " 
9 


§  55-  Effect  of  Putting  the  Pyramid  in  a  Sphere.  95 
20613  X      — q  =  3053-^^2-|-  Circumference  of  pyramid. 


X      -^  =  1526.811+       - 

216  -^  '  2 


u 


(( 


I 


X    ^^=  763-407+     ^ 

X     ^4=   3S.-7037+     3 


U 


"      X    -^^=  190.S518  ~ 

1728  -^        -^  JO 

288  18 

"      X77^=  34-3533+  -60 

«    x-^=  17.1766+  - 

34560  320 


(( 


"      X^=       85SS3+   -^ 

69120  JOT        g^Q 

The  enlargements  are  to  be  obtained  by  use  of  the  same 

factors,  on  the  enlargement  of  20612  to  2062647001,  thus: 

6561  X  100-^20612=31.8309722  + 
31.830972  X  12  =  381.9716664+ 

864 
381.97166+  X    -~z-  =  20626.47001+ ; 

which  last  result  is  the  enlargement  on  the  Parker  primary- 
circumference. 


SECTION  III. 

EFFECT  OF  PUTTING  THE  PYRAMID  IN  A  SPHERE,  PRELIMINARY 
TO  GIVING,  OR  WORKING  OUT,  ITS  FURTHER  MEASURES  ;  AND 
STATED  AS  HYPOTHESIS  OR  THEORY.  OBTAINING  THE  NUM. 
BER   VALUE    21633O. 

(§  55-)  Thus  there  has  been  displayed  the  elements  for 
the  construction  of  the  pyramid ;  the  enlargement  on  the 
same,  with  the  reason  therefor;  the  standard  measures, 
and  actual  measures  thereof  as  enlargements,  or  variations, 
on  the  standard ;  as  also  of  the  three  elements  of  the 
length,  breadth,  and  height  of  the  king's  chamber. 


96 


Construction  of  the  Great  Pyramid. 


55' 


It  is  thought  there  is  a  reason  for  the  pyramidal  shape  of 
the  structure  ;  and  because  the  use  of  it  in  that  shape  can 
be  made  instrumental  in  the  production  of  a  numerical 
value,  which  seems  to  be  recognized  and  made  use  of,  or 
rather  worked  with  reference  to,  by  the  architect,  in  most 
of  the  governing  lines  of  the  interior  work,  it  is  thought 
best  to  commence  with  the  development  of  the  number 

216330 
as  a  result  of  placing  a  -pyramid^  in  terms  of  the  original 
Parker  measures,  in  a  sphere.  From  this,  as  will  be  seen, 
some  very  extraordinary  numerical  relations  arise,  which 
harmonize  with  the  supposed  object,  or  genius  of  the 
structure. 


{a.)  Let  A  D  B'  represent  a  vertical  meridianal  section, 
and  AB  B'  a  transverse  vertical  section  (cutting  in  the  cor- 
ners) of  the  pyramid.      Let  D  B'  —  -  side  of  base,  and 

BB'  =  —  diagonal  of  base.     Then, 


Height 


(standard),  AB'  =  656i 


§55"  Effect  of  Putting  the  Pyramid  in  a  Sphere.  97 
— Base  side  (standard),  DB'  =  5i53 


BB'=VDB'^X2         ««  =7287.44248+ 

To  get  this  pyramid  in  a  sphere,  AB'  must  be  produced 

to  such  a  length,  that  with  some  point,  as  O,  as  a  center, 

and  with  O  A  as  a  radius,  a  circle  may  be  described  which 

will  cut  in  the  points  A  and  B.     This  can  be  done  because 

B  B'  is  a  mean  proportional  between  A  B'  and  some  length 

,  .  ,      .        AB'4-x 
X,  which  gives   • =  radius  required. 

This  radius  equals  7327.6588172  +  . 
As  B  B'  is  longer  than  A  B',  addition  must  be  made  to  A  B' 
to  get  this  radius.  The  difference  between  them  is 
726.44248+  ;  and  this  added  to  AB'  gives  the  7287.44248. 
Now,  though  A  B'  has  been  increased  to  equal  B  B',  it  still 
is  not  the  radius  required ;  because,  by  difference  in  posi- 
tion, AB'  thus  increased,  taken  as  a  radius,  can  not  inclose 
the  pyramid.     A  further  distance  is  required. 

The  true  value  is  as  stated,  7327.6588172+. 
The  difference  between  this  and  A  B'  increased  as  above 
is  40.216330+. 

Now,  let  B  B'  be  increased  by  the  whole  number  of  this 
last  difference,  viz.,  40;  then  there  will  remain  as  between 
the  true  radius,  7327.6588+,  of  the  circle  inclosing  the 
pyramid,  and  H  H',  the  numerical  value, 

216330, 
as  a  final  difference. 

216330  Found  as  an  Elliptical  Difference. 

(d.)  There  are  two  ways  to  take  up  or  represent  an  el- 
liptical property  :  one  is  to  measure  out  from  a  common 
central  point  to  the  end  of  the  major,  or  minor,  axis  of 
the  ellipse  ;  the  other  is  to  take  a  true  circle,  and  exhibit 
the  same  difference  al  the  center,  on  the  quadrant  lines. 
Here  the  latter  plan  seems  to  have  been  adopted : 

AO=  7327.6588172 

HH'=  7327.442487 


Difference,  .216330; 


98  Construction  of  the  Great  Pyramid.      §  56. 

which  thus  introduces  the  property  of  an  ellipse,  as  con- 
nected with  the  sphere,  taken  up  or  represented  at  the  cen- 
ter thereof. 

True  Pyramid  springing  from  the  Pyramid  placed  iti  the 

Sphere. 

(c.)  It  is  seen  that  this  pyramid  thus  placed  in  the 
sphere,  is  composed  from  the  original  Parker  elements,  in 
numbers.  Now,  any  pyramid  taken  off  this  by  a  base 
line,  as  C  C,  drawn  parallel  with  B  B',  will  be  proportional 
in  all  its  elements  with  the  pyramid  inclosed  in  the  sphere. 
On  the  pyramid  lines  thus  placed  in  the  sphere,  another  is 
required  to  represent  the  Parker  formulas — 

20612  X  -2  =  36643.55+* 

42 
6561  X-2  =  1 1664.  ; 

in  which  36643. 55-I-  is  to  represent  the  circumference  of 
the  base,  and  11664  is  to  represent  the  height.  This  can 
be  done  :  reducing  the  values  to  feet,  equals  for  circumfer- 
ence 3053+  feet;  or,  for  base  side,  D'C  x  2  =  763.4074+ 
feet  (standard  measure);  and,  for  height,  11664 -^- 12  = 
972  for  diameter,  and  972  -^  2  =  486  feet  (standard  meas- 
ure) for  radius  or  height ;  whereby,  on  the  lines  of  the  first 
pyramid,  constructed  from  the  original  Parker  numbers, 
another  pyramid  is  made  to  spring  from  the  same  original 
numbers  in  terms  of  the  Parker  formula,  for  obtaining  in 
366.4355,  as  he  says,  "the  exact  time  of  the  passage  of 
the  earth  around  the  sun  over  the  value  of  a  complete  circle 
in  space  in  circular  days."  The  enlarged  meastires  of  the 
^yrai7iid  proper  are  to  be  had  by  extending  the  height  and 
standard  base  lilies. 

Solar  Year  Value  obtained  from  —  Base  Side  of  Pyramid, 

and  the  Sine  of  30°. 

(§  56.)  It  is  to  be  noted  that  the  north  base  line  of  the 
great  pyramid  is  located  on  the  actual  parallel  of  30°  north 
latitude.     Let  it  be  assumed  that  the  sphere  taken  was  in- 


§  56.  Effect  of  Putting  the  Pyramid  in  a  Sphere.    99 

tended  to  represent  the  earth;  that  by  the  difference  taken 
up  at  the  center,  as  shown,  a  datum,  numerically,  of  the 
elliptical  property,  or  of  an  elliptieal  property,  of  the 
earth's  shape,  or  of  its  spheroidal  character,  was  intended; 
and  then,  that  the  line  of  30°  was  intended  as  a  point  to 
work  to  in  the  elaboration  of  the  problems  intended  to  be 
displayed  as  measuring  the  earth  and  the  planetary  orbits. 
A  use  of  this  can  be  made  manifest. 

{a.)     The  standard  length  of  D'C,  or  -  base  side  of  the 

pyramid,  is — 

(i.)     381.70370+  feet. 
The  half  of  this  is — 

(2.)     190.851851+  feet. 
In  the  circle  of  this  diagram  is  represented  the  pyramid 

taken  at  the  standard  height  and  -  base  side,  or  486  feet, 

and  381.7037-f-  feet,  respectively,  as  a  proportional  part  of 
the  ideal  pyramid  drawn  in  the  sphere.  The  actual  pyra- 
mid is  an  enlargement  on  these  values  of  486.341x8+  feet 
for  height,  and  381.97166+  feet  for  half  base  side ;  and,  to 
effect  this,  the  height  will  project  beyond  the  circle  .34118 
of  a  foot,  and  the  base  line  will  be  projected  for  the  other 
differences. 

The  radius  of  the  standard  circle  is  610.638234+  feet. 

Add,  for  enlarged  height,  .341181+    " 

(3.)     Enlarged  radius,  610.979415+  feet. 

ibi)  From  the  center  O  of  the  sphere  (preceding  figure), 
draw  the  radius  line  O  F,  to  intersect  the  parallel  line  of 
30°,  at  F  on  the  sphere,  taken  as  thus  enlarged.  The  dis- 
tance O  D",  where  this  radius  line  is  found  to  intersect  the 
inclined  side  of  the  pyramid,  is  found  to  be  381.22807  feet, 
as  follows  :  The  angle  A  D"E  =  51°  51'  I4"5  ;  the  angle 
E  D"0  =  30°  ;  then  the  angle  A  D"0  =  81°  51'  i4"5  ;  the 
angle  D"A  E  =  38°  08'  45"5  ;  and  the  angle  AO  D"  --  60° ; 
then — 


lOO         Construction  of  the  Great  Pyramid.       §  56 

Shi.  81°  51'  14"  5  9-995595 
Sin.  38°  08' 45"  5  9-790754 
Log.  610.979415  2.786026 
Log.  381.22807  2.581185 
If  this  is  taken  as  the  radius,  then  the  value  of  the  sine  line 
of  30°,  or  O  E,  will  be, 

(2.)  190.614035+  feet. 
Compare  this  value  of  sine  of  30°,  with  the  corresponding 
value  of  standard  one-fourth  base  side  [(<^)(2.)]»  or, 
190.851851+  feet;  and  let  it  be  taken  that  the  object  has 
been  to  get  the  difference  between  these  values,  as  to  their 
decimals,  for  use,  so  that : 

(3.)  190—  I  851851  —190  —  I  614035  =  190—  I  237816. 
The  uses  of  this  remainder  are  in  exceeding  great  harmony 
with  the  scheme  supposed.  190.85 185 1  +  is  the  standard  value 

of  the  —  the  base  side  of  the  pyramid,  or  190.851851  X  4^r 

4 
or  16,  equals  the  standard  circumference  of  the  pyramid  in 

feet,  or  36643.555-}-  inches,  where  the  height  of  the  pyr- 
amid is  to  this  value  as  radius  is  to  circumference  of  a  cir- 
cle.    As  to  the  use  of  the  variation  found  : 
(4.)     190.237816  feet  equals,  in  inches,      2282.853792. 
and — 

(5.)     2282.853792  X  4^5  or  16,  =,  in  inches,  36525.660672, 
or,  in  tenths  of  inches,  365256.60672, 
as  a  result  from   the  use  of  this  difference  between   the 

standard  —base  side,  and  the  sine  value  of  30°  as  taken. 
4 
(c.)     36525  is  numerically  taken   as   the    correct  solar 

year  day  value,  or  circle,  as  used  in  the   calendars  ;  but 

this  carries  it  to  a  greater  exactitude,  for  this  value  is  in 

tenths  of  inches,  365256.6067-f 

The  true  and  exact  solar  year  value  is  365256.3835 

Difference,  000000. 2232 -f- 

or  17"  in  a  year's  time  :  so  close  an  approximate  that  5000 
years  would  have  to  elapse  to  require  the  intercalation  of 
I  day,  for  correction  of  the  calendar. 

Note  on  §  56. — The  results  of  thus  putting  the  pyramid  in 


§  57-  Effect  of  Putting  the  Pyramid  in  a  Sphere,  ioi 

a  sphere  can  be  shown  by  diagram.  The  base  of  the  pyr- 
amid proper  is  36643.55  inches,  from  which  numerical 
vahie  Mr.  Parker  derives  the  exact  solar  year  period.  The 
side  of  the  square  base  is  763.4074  feet.  This  divided  by 
2  is  381.7037+  feet;  and  this  by  2=190.851851  feet: 
the  very  division  on  which  comparison  is  made  for  the  dif- 
ferential of  190.237816,  by  running  a  radius  to  30°,  on  the 
circle  of  iYm  pyramid  enlarged.     It  is  tlius  seen  that  this  is 

a  method  of  working  the  differential  on  the  —  base  side, 

&  2 

and  the    -  base   side,  of  the   pyramid.     190.614035   being 

4 
5/«r  of  30°,  then  190.614035  X  2=^381.22807  feet,  becomes 

the  side  of  a  square  measured  on  this  circle :  so  that  this  is 
a  square  of  comparison  with  that  of  the  base  of  the  pyramid, 
in  its  seen  division,  to  obtain  a  differential  to  procure  the 
solar  year  value.  This  division  of  the  square  base  of  the  pyr- 
amid ,  divides  it  into  16  squares  ;  1 2  around  the  circumference 
and  4  in  the  midst,  framed  on  tzuo  lines  crossing  in  the 
center.  This  is  exactly  the  square  framed  for  the  Garden 
of  Eden,  and  the  encampment  of  the  Israelites,  showing 
that  the  Hebrew  idea  is  just  that  of  the  Egypdans.     Now, 

the  square  base  of  the  p3'ramid  is  the  zodiac.     The  —  of 

this  square  is  a  variation  on  that  square  in  a  circle  obtained 
by  putting  the  ideal  pyramid  in  a  sphere,  cutting  in  the 
parallel  of  30°,  and  thus  obtaining  the  solar  year,  as  the 
value  of  the  zodiac.  But  the  sphere  itself  is  representa- 
tive of  the  earth,  the  diameters  of  which  are  to  be  worked 
out  co-ordinately  with  the  time  value  of  the  zodiac,  and  in 
and  from  the  tame  data.  Was  there  ever  a  more  magnifi- 
cent conception?  The  data  for  exact  computation  are  the 
governing  ones,  and  the  architect  is  cunningly  blocking  out 
the  cosmic  work  architecturally. 

Equatorial  and  Polar  Diameters  of  the  Earth  obtained. 

(§  57.)     It  is  seen  that  this  very  exact  solar  year  numer- 
ical value,  in  tenths  of  inches,  is  architecturally  obtained  as 


I02        Construction  of  the  Great  Pyramid.       §  57. 

a  variation,  by  difference,  on  366435. 5 -f- in  tenths  of  inches, 
or  the  standard  circumference  of  the  pyramid  proper, 
which  value  as  366.4355  is  the  ver}'  value,  which,  under 
his  problem  of  three  revolving  bodies,  John  A.  Par- 
ker raises  from  these  very  original  elements  of  his  quad- 
rature (which,  under  the  present  application,  give  the  pyra_ 
mid  in  the  sphere,  whence  the  real  pyramid  is  taken)  as 
"  the  exact  value  of  the  passage  of  the  earth  about  the 
sun,"  etc.  Now,  if  under  the  geometrical  conditions  framed 
iri  §  55  («)j  and  with  the  data  obtained  of  3664355  +  ,  and 
the  elliptical  value  numerical  of  216330-I-,  taken  up  at  the 
center  of  the  earth,  the  actual  miles  numerical  value  of  the 
earth's  diameters  can  be  worked  out,  it  would  seem,  almost, 
that  the  design  of  the  architect  must  be  being  reproduced, 
though  perhaps  in  a  stumbling  way,  and  lacking  in  the  re- 
finements, and  proper  details,  by  which  he  almost  undoubt- 
edly was  working  out  planetary  exactitudes  as  to  size  and 
motion  through  geometrical  elements,  under  a  co-ordinat- 
ing system  of  construction  and  of  notation.  As  a  fact,  by 
a  very  beautiful  calculation  through  these  very  means,  the 
equatorial  and  polar  diameters  of  the  earth  can  numerically 
be  obtained. 

{a.)     Let  the  values  of  the  earth's  diameters  be  taken 
at,  for 

(i.)     Equatorial  diameter,  41.854.174+    feet, 

And  another  at  some  other  point,  41.739.954+        " 

758 
The  difference  is  114219.   —        " 

If  the  larger  diameter  be  divided  by  this  difference  the  quo- 
tient will  be  366.4355  +  ,  and  this  is  numerically  that  value 

42 
springing   from    the    Parker   elements   of    206.12  X   ^  = 

o 

366.4355+,  which,  as  he  says,  is  "  the  exact  value  of  the 
passage  of  the  earth  about  the  sun  over  one  complete  circle 
in  space  in  circular  days ;"  and  used  otherwise  for  pyra- 
midal purposes,  is  in  36643.55  inches  the  standard  circum- 
ference of  the  pyramid. 


§  57'  Effect  of  Putting  the  Pyramid  in  a  Sphere.  103 


[The  question  has  been  raised,  by  what  authority  Parker  points 
this  value  at  366.43554-5  and  in  truth  he  is  not  clear  as  to  this. 
But  a  way  can  be  shown,  by  throwing  the  values  from  inches  into 

200 1  2 

feet,  thus: =  i. 71 766  feet,  or  the  value  of  i  cubit.   120  cubits, 

12000  '    ' 

12  4^ 

then,  is  206. —  feet,  and  this  X  -^^  =  366.4355  +  ?  as  the  Parker 

time  day  value,  thus  shown  to  be  in  British  feet.] 

In  this  formulation,  since  the  smaller  diameter  taken  is 
less  than  the  dividend  by  the  amount  of  the  divisor,  the 
quotient  of  the  smaller  divided  by  the  difference,  will  be 
one  less  than  the  first  quotient,  or  365.4355-I-:  There  re- 
sults : 

(2.)  366.4355+  )  )4i-854-i74+  feet, 

>   X  114219.758  =    > 

365-4355+)  MI-739-954+    " 

where  the  products  are  the  return  of  the  diameter  values  of 

the  earth  as  taken. 

7c;8 
But  114219.^—  feet  equal  21.63253+  miles  British,  and 

the   difference  taken  up   at  the  center  of  the    sphere   as 

shown,  was,  numerically,  21.6330;  which,  if  it  be  taken 

as  representing  this  miles  value  of  difference,  shows  a  dis- 

4 
crepancy  of  — ^^—  of  a  mile,  or  of  2  feet,  as  the  difference 

'  -  lOOOO 

of  the  earth's  diameter  as  taken. 

[Here  it  will  be  seen  that  41854174  feet  25,  to  all  intents,  the 
equatorial  diameter  of  the  earth.  This  being  so,  the  numerical 
datum  of  216330  found  as  equal  to  a  miles  elliptical  difference 
value  may  be  one  assumed  as  being  thus  found,  and  on  which,  as 
one  true  value  is  already  obtained,  the  other  may  be  had.] 

{d.)     It  has  been  shown  that  36643.55+  is  obtained  by 

use  of  20612  X  ^-     Since  21632.53  is  numerically  nearly 

the  same  as  2061200,  and  5'et  is  taken  as  a  miles  value, 

transformation   may  be   made  of^  21.63253   into  the  terms 

.2 
of  the  formula  20612  x  ^»  or  by  use  of  the  factors  3  and 


As  it  appears  that- 
3' 


(I.)     206.12  X  :;j=  366.4355+, 


I04        Construction  of  the  Great  Pyramid.      §  57. 

so  it  seems  that — 

(2.)     21.63253  X  ^=  365.04894+. 
Substitute  this  value  in  {a)  (2),  and,  formulating,  we  have — 
4^ 


(3.)     366.4355+  X  365-04894  X  ^=  7926.92686, 

where,  in  place  of  the  resultant  value  appearing  in  feet,  it 
is  now  produced  in  juilcs  British,  of  the  equatorial  diam- 
eter of  the  earth  ;  and — 

4^ 


(4-)     365-4355  X  365-04894  X  ^=  7905. 2943+, 

where  the  result,  in  place  of  feet,  is  now  produced  in  miles' 
value  of  the  other  diameter,  as  taken. 

{c.)     But  now  there  appears  a  co-ordination  of  values ; 
for,  since,  by  the  above  formulation,  {b)  (4),  it  is — 

365.4355+  X  365.04894-, 
this  is  precisely  the  same  as  the  square  of  the  mean  of  these 
values ;  thus — 

4^ 


(I.)    365-24225   X  ^=7905-2943+; 

and  hence,  for  the  larger  diameter,  there  is — 


(2.)  365.24225- -1-36504894  X  looooo  X— =  7926.92686-]-. 

In  these  last  formulations,  365.24225+  is  the  value  of 
the  mean  solar  year. 

Note,  that  7926.9268  -^  24  =  330.2886,  and  by  Professor 
Smyth  the  length  of  passage  through  ante-chamber  to 
king's  chamber,  from  edge  of  great  step,  is  330. 3d=  inches  ; 
and  as  it  is  seen  that  this  miles'  value  is  a  time  value  through 
the  mean  solar  year,  the  key  of  this  passage-way  measure 
seems  to  be  found,  as  a  co-ordinating  one,  of  these  very 
elements. 

{d.)  But  thus  far,  in  these  formulations,  the  equatorial 
value  alone  has  been  obtained.  In  §  56  {b),  above,  it  is 
shown  that  the  sine  value,  or  O  E,  of  30°,  compared  with 

the  —of  the  base  side  of  the  pyramid,  taken  at  the  standard, 
4 


§  57-  Effect  of  Putting  the  Pyramid  in  a  Sphere.  105 

gives  for  use  the  value  of  190.237816-}- feet,  which  reduced 
or  scaled  to  tenths  of  inches,  and  multiplied  by  4*,  or  16, 
to  get  the  variation  on  the  entire  circumference  of  the  pyra- 
mid of  366435.5 -|-,  in  tenths  of  inches,  the  standard  value, 
gave,  as  a  result,  the  almost  exacdy  true  solar  year  value  of 

/;/  thousandths  of  days ^  365256. 3S3  +  . 
The  elements  there  used  are  directly  connected  with  those 
herein  used — viz.,  the  circumference  of  366435. 5+  is  so  va- 
ried as  to  produce  365256,  the  true  solar  year ;  whereas  here 
the  mean  solar  y<:ar  value  has  been  used,  and  that  as  com- 
ing from  use,  in  part,  of  the  same  value  of  3664355-!-.  The 
miles  value  is  numerically  represented  as  a  difference  taken 
up  in  the  center  of  the  sphere,  in  which  the  pyramid,  in 
the  original  Parker  numbers,  has  been  placed.  From  this 
same  center  the  radius  line  of  30°  is  taken,  which  gives  the 
sine  value  of  190.614035,  whence  190.337+  was  obtained. 

Make  use  of  these  values  so  connected  : 

(i.)  Standard  circumference  value  in  inches,  36643.55-}-. 

(2.)      190.237816  feet  (the  variation  on  the —  side  of  the 

4 
pyramid,  used  above)  X  4  =  760.9512  (the  variation  on  the 

value  of  the  full  base  side  of  the:  pyramid). 

(3.)     Now,  if  the  —  of  this  last,  in  a  scale  of  inches  for 

feet,  or  76.09512-f-,  be  taken  from  366.4355-f ,  or  the  — 

of  the  full  circumference  of  the  base,  in  inches,  the  differ- 
ence is  290.34043+  ;  and  let  this  be  considered,  on  a  scale 
of  feet  for  inches,  as  the  number  of  times  the  difference 
between  the  equatorial  and  polar  diameters  is  taken,  in- 
stead of  366.4355  +  ,  the  number  of  times  the  difference  be- 
tween the  diameters  already  used  was  taken. 

(4.)     Then  the  larger   diameter   divided   by  this  value 
will  give  the  new  difference,  the  ultimatum  sought,  or, 

41854174+  --  290.34043  =  144x55.5, 
in  place  of  114219.758+ 

as  already  taken  [§  57  («.)]. 


io6        Construction  of  the  Great  Pyramid.      §  57. 


(5.)  Then  the  larger  diameter  less  this  difference  will 
give,  say,  the  numerical  value  of  the  -polar  diameter,  or, 

41854174    feet, 

less  144155 

equals  41710019       " 

or,  in  miles  British,     7899.6248 

In  fact,  this  resultant  value  is  to  all  intents  the  true  value 
of  the  polar  diameter  of  the  earth.  Comparison  gives  as 
follows  : 

(6.)     Equatorial  diameter  assumed,  41854174+  feet. 
As  ascertained,  41852864+ 

Difference,  1310+ 

Polar  diameter  assumed,  41710019+ 

As  ascertained,  41708710+ 

Difference,  1309+ 

Note. — While  there  is  enlargement  as  seen,  yet  this  scarcely 
affects  the  difference  of  the  diameters,  thus : 

Equa.  found,       7936.9260  miles. 
Polar,     "  7899.6248      " 

Difference,  27.3020      " 

Equa.  received,  7926.6789     " 
Polar,        "         7899,3768     " 

Difference,  27.3021      " 

Now,  while  there  is  very  much  elaboration  in  the  work- 
ing out  of  the  polar  value  results,  in  the  way  of  scaling  of 
measures,  it  must  be  borne  in  mind  that  in  architectural,  or 
object,  or  block  building  in  of  such  problems,  just  this 
class  of  work  is  to  be  expected  of  necessity  ;  therefore,  this 
elaboration  is  in  full  harmony  with  the  genius  of  the  prob- 
lem making  of  the  entire  pyramid  structure — in  fact,  it 
may  be  expected  in  a  far  greater  refinement  of  elaboration 
than  here  shown,  as  is  testified  to  by  the  greater  and  greater 
amount  of  subdivision,  and  change  of  scales,  as  one  pro- 
gresses from  the  outside  to  the  coffer  in  the  king's  cham- 
ber ;  also,  by  the  refinements  of  measures  displayed  on  the 
walls  and  in  the  works  of  the  ante-chamber,  the  recess  of 
the  queen's  chamber,  and  the  wall  courses   of  the  king's 


§  57-  Effect  of  Putting  the  Pyramid  in  a  Sphere.  107 

chamber.  It  seems  evident  that  just  this  nature  of  work- 
ing of  values  was  made,  but  unfortunately  for  us,  our  high- 
est efforts,  at  present,  can  only  reach  to  a  study  as  to  the 
keys  of  the  method  of  calculation  employed.  The  above 
may  be  the  exceedingly  detailed  elaboration  of  results 
somehow,  by  some  architectural  device,  plainly  set  forth 
in  the  concrete,  in  natural  exactitudes. 

All  these  results  depend  upon  the  placing  of  an  original 
pyramid  in  a  sphere,  in  the  Parker  values,  giving  the  ele- 
ments shown,  and  especially  the  final  difference  of — 

216330. 
As  to  the  extraordinary  combinations  shown,  all  harmo- 
nious among  themselves,  and  in  full  accord  with  the  genius 
of  the  whole  pyramid  system,  as  it  has  been,  and  as  it  will 
be  seen,  in  its  further  developments,  they  seem  to  claim 
recoo-nition  as  the  real  mental  intent  of  the  architect,  rather 
than  as  the  results  of  a  happy  inventive  faculty.  It  is 
thought  that  it  is  almost  impossible  to  conceive  of  the  pos- 
session of  a  power  of  inventing  such  co-ordinating  harmo- 
nies as  are  above  set  forth,  especially  where  all  the  steps 
are  so  fitting  to  architectural  work,  where  the  object  would 
be  to  obtain  correct  numerical  data,  which  obtained,  the 
harmony  of  kinds  of  measure  would,  as  has  been  said,  be 
preserved,  by  changes  of  the  scales  of  measure. 

NOTE  TO  §  57   {d). 

The  processes  stated  are  somewhat  strengthened,  as  be- 
ing rightly  taken,  from  the  following  :  The  circumference 
of   base    of    the    pyramid    is    36643-5555+    inches,    or 

2 
3053.629629  feet.     Take  -^of  this.     It  is — 

(i.)     610.725925+  feet; 
whereas,  the   radius   of  the    sphere,  as    shown,  is    7327. 
658816+  inches.     This  reduced  to  feet,  is — 

(2.)     610.63823  feet. 
Raise  both  to  pyramid  circumference  values — 
(i.)  becomes  3053.6296+  feet. 
(2.)  becomes  3053.1911+  feet. 


io8        Construction  of  the  Great  Pyramid.      §  58. 

Raise  both  to  radius  of  sphere  vakies — 

(i.)  becomes  7328.711 1096  feet. 
(2.)  becomes  7327.658816  feet. 
The  placing  the  pyramid  framed  from  the  original  num- 
bers in  a  sphere  is  evidently  done,  for  one  thing,  to  get  a 
variation    on  the  circitmfercncc  of  the    base  of  the    real 
pyramid. 

Now,  7327.658816  ^  20  =  366.3829416,  as  a  variation 
on  366.4355  +  .  Take  the  earth's  equatorial  diameter,  as 
received,  at  7926.67897  miles.  Then,  7926.67897  -h  Z'^d-- 
3829416  =  21.6349-f-  n^iles,  different,  numerically,  from 
the  216330  taken  up  as  an  elliptical  difference  in  the 
sphere  .0019. 

Such  correlations  can  not  be  accidental.  It  goes  to  prove- 
that  the  processes  are  those  of  nature,  and  that  the  pyra- 
mid constructors  knew  the  processes. 

(§  58.)  If  the  conclusion  be  well  taken,  that  the  archi- 
tect of  the  pyramid  recognized  in  this  value  of  216330,  nu- 
merically, a  miles  difference  in  value  of  earth's  diameters, 
whence,  with  the  solar  year  time  values,  the  earth's  actual 
equatorial  and  polar  diameters  were  numerically  obtainable, 
the  grades  of  measure  springing  from  the  inch  and  foot 
British,  and  these,  with  the  cubit,  from  the  Parker  ele- 
ments, then  the  overwhelming  importance  to  man,  as  man, 
of  this  fact,  is  explainable. 

This  measure  is  just  that  one  that,  with  the  ancients,  seems 
to  have  stamped  the  whole  system  as  natural  or  divine, 
i.  e.,  showing  that  man  was  but  dealing  in  measures,  in 
some  sort  shadowing  forth  mechanical  principles  of  con- 
struction, which  it  had  pleased  the  Creator  of  all  things  to 
adopt  as  the  law  of  creation.  Man  seems  capable,  for  in- 
stance, of  arriving,  by  use  of  his  own  powers,  to  a  knowl- 
edge of  the  abstract  truths  of  this  system,  just  as  is  evi- 
denced by  the  works  of  John  A.  Parker.  By  observation, 
the  application  of  this  system  to  the  measures  of  natural 
periods  of  time  could  be  arrived  at.  But  if  the  attempt 
was  to  be  made  to  apply  the  system,  so  that,  in  the  planet- 


§  57-  Effect  of  Putting  the  Pyramid  in  a  Sphere.  109 

ary  system,  measures  of  lime  were  to  be  co-ordinated  witli 
the  actual  material  extension  of  the  planets,  before  man 
could  recognize  or  realize  this,  it  would  become  necessary 
for  him  to  establish  some  unit  of  measure  for  -practical 
use  as  an  inch,  for  instance,  marked  on  a  rod  or  rule. 
Whatever  such  measure  he  might  adopt,  he  would  have, 
of  necessity,  to  abide  by  its  results.  What,  therefore, 
would  be  the  chances,  that,  in  the  practical  adoption  of 
such  a  measure,  as  by  the  averaging  of  barley-corns,  or 
taking  the  measure  of  the  average  length  of  the  thumb, 
he  would  actually  take  that  very  measure  by  which  the 
recognition  that,  in  mechanical  construction,  the  planets,  by 
law,  were  to  co-ordinate  in  measure  with  their  times,  in 
terms  of  measures  growing  out  of  a  common  system,  would 
or  could  come  to  him  ?  The  answer  must  be  that  they 
would  be  millions  to  one  against  the  hitting  on  the  exacti- 
tude. Therefore,  a  measure  being  in  use,  and  found  to 
answer  this  purpose  and  end,  would  be  the  proof,  above 
all  others,  of  man's  possession,  however  he  came  by  it,  of 
the  actual,  practically  adopted,  material  measure,  by  which, 
under  the  lazv  of  creation,  the  Creator  mechanically  or 
materially  constructed  the  earth  and  all  other  planetary 
bodies. 

(§  59.)  As,  however,  to  this  number,  among  other 
places,  it  is  found  that  this  very  numeral,  216330,  found,  at 
first,  as  notating  the  difference  of  the  elliptical  diameters 
of  the  earth  in  miles  (which  diameters  are  measurable  in 
terms  of  the  square  of  the  mean  solar  year  period,  and  by 
means  of  the  true  solar  year  value),  again  develops  itself 
quite  a  number  of  times  in  very  important  measures,  one 
of  which  is  on  the  level  of  the  base  of  the  grand  gallery, 
the  approach  to  the  king's  chamber,  where  the  earth  meas- 
ures and  the  earth  time  measures  come  together  to  be 
measured  on  a  circumference  (of  subdivisions)  of  the  num- 
ber 6,  as  of  360°,  growing  out  of  the  factor  6  (and,  by 
change,  on  a  square  of  6  X  6,  to  co-ordinate  round  witli 
plane  measure),  which  is  the  circumference  to  the  height 
of  this  chamber  as  diameter ;  which,  again,  springs  from 


no        Construction  of  the  Great  Pyramid.      §  60. 

a  circumference  of  i  to  a  diameter  of  318+,  which  318-j-  is, 
or  was,  the  Gnostic  value  of  the  term  Christ,  and  was  what 
was  intended  b}^  the  318  trained  servants  or  circumcised 
men  of  Abraham,  in  the  Hebrew  Bible.  And  all  this 
comes  directly  in  harmony  with  the  elevation  of  the  floor- 
level  of  the  king's  chamber  above  the  base  of  the  pyra- 
mid, which  is  137.509+  feet;  for  this  value  is  in  inches 
1650. 116+,  which  is  the  diameter  to  a  circumference  of 
5184,  which  is  the  characteristic  value  of  the  subdivisions 
of  a  solar  day  into  thirds^  that  full  value  being  5184000'" ; 
which  value,  again,  is  only  evenly  divisible  into  the  acre 
value  of  the  British  land  measures,  which  acre  value  is  the 
base  of  the  mile's  British  value. 


SECTION  IV. 

THE    king's    chamber    AND     THE    SQUARE     ROOT    OF    THE    SOLAR 

YEAR. 

(§60.)  In  §  57  {c.),  [d.],  it  is  seen  that  the  use  of  the 
216330,  connected  with  the  pyramid,  involves  the  numeri- 
cal value  of  the  earth's  diameters  in  miles,  in  terms  of  the 
square  of  the  year  value  in  days ;  and  it  is  stated  that  the 
king's  chamber  levels  involve  this  number.  In  §  51,  §  53 
{a),  it  is  to  be  seen  that  the  height  of  the  king's  chamber  is 
a  diameter  to  a  circumference  of  60;  and  involves,  agree- 
ably to  the  measures  of  that  chamber  coinciding  with  the 
Hindu  formula  for  obtaining  sines,  cosines,  tangents,  co- 
tangents, and  planetary  orbits,  as  per  Mr.  Bentley,  the  cir- 
cle of  360°,  with  its  divisions  for  measuring  the  solar  year, 
and  also  the  hour  values  on  the  earth's  circumference  in 
miles.  The  height  of  the  king's  chamber,  spoken  of,  is  in 
feet,  and  is  a  diameter  value  of  19.0985+  to  a  circum- 
ference of  60.  This,  in  inches,  would  give  a  circumfer- 
ence of  720,  and  this  squared,  or  the  area  of  that  height, 

equals  518400,  or  the  — of  the  subdivision  of  a  solar  day 


§  6i.  Sq^  Root  OF  Solar  Year  IN  King's  Chamber,    in 

I 

in  thirds.     The      of  720  is  144,  or  the  square  of  12.     The 

height  of  the  chamber  is  divided  into  5  courses  of  masonry, 
and  though,  unevenly,  on  account  of  a  difference  caused 
by  filling  in  on  the  lower  course,  may  be  taken  as  symbol- 
izing the  use  of  the  number  5,  as  thus  used  (also,  —of  60 

is  15,  as  of  15°  to  an  hour's  time  on  the  earth).  The  above 
division  is  exactly  that  of  the  Egyptian  equatorial,  accord- 
ing to  Seyffarth,  and  borrows  strength  from  a  peculiarity 
of  the  Hebrew  Bible  numerical  system.  The  word  Adam 
is  144,  and  Elohim  (in  a  circle)  reads  31415.  But  the  radi- 
cal of  Elohim  is  El,  which  is  31.  The  solar  day  value  is 
5184  in  one  of  its  subdivisions,  and  this  is  a  multiple  of 
144.  Subtract  the  value  of  El,  or  31,  from  144  and  5184, 
thus — 

(I.)  144  —  31  =  113.  (2.)  5184  —  31=5153, 
and  in  (i.)  there  remains  a  diameter  to  a  circumference  of 
355,  which  is  the  Hebrew  word  Shanah,  for  lunar  year ; 
and  in  (2.)  there  remains  the  Parker  area  of  the  circle  in- 
scribed in  the  square.  All  these  are  pyramid  numbers, 
and,  as  seen,  involve  the  value  of  a  day,  year,  mile,  and 
foot.  Thus,  144  and  5184  are  the  extremes  of  the  British 
long  and  land  measures,  inasmuch  as  one  is  the  square  of 
12,  and  the  last,  which  is  the  number  of  inches  in  the 
square  yard  multiplied  by  4,  is  evenly  divisible  only  in  the 
acre  value  in  inches,  which  acre  value  is  the  base  of  the 
miles  value.  Thus,  in  this  king's  chamber,  is  a  mingling 
of  co-ordinations  of  use  of  the  inch,  foot,  yard,  and  miles 
value,  with  those  of  days  and  years.  One  means  is,  as 
seen,  by  means  of  the  square  of  the  solar  year  value  ;  and 
the  number  216330,  v^  hich  involves  this  use,  is  also  made 
use  of  in  the  levels  of  approach  to  the'  king's  chamber,  as 
is  shown  in  §  75,  thus  bringing  this  relation  of  the  square 
of  the  solar  year  to  bear  upon  that  chamber  in  the  use  of 
its  dimensions. 

(§  61.)     (i.)    Professor   Smyth    discovered    a    persistent 
variation  in  the  lengths  of  passage-ways  and  dimensions 


112         Construction  of  the  Great  Pyramid.       §  62. 

of  the  chambers  and  of  the  coffer;  that  is,  they  all  pre- 
sented these  variations  on  a  mean  of  measure  taken  as  a 
standard.  He  was  forced  to  the  conviction  that  this  was 
purposed,  and,  if  so,  it  was  as  a  scheme  for  the  exhibition 
of  variation  of  measures.  The  ability  of  the  workmen  to 
work  to  exactitude  in  these  respects  was  amply  displayed, 
and  especially  in  the  king's  chamber,  whose  walls  are  in 
the  hardest  granite,  polished  to  the  highest  reach  of  art, 
and  whose  joints  are  to  be  likened  to  the  thickness  of  gold- 
leaf. 

(2.)     The  king's  chamber  is,  as  shown — 

in  height,     19.0985+  feet. 
(a.)     The  true  solar  year  is,  365.2563835 

(5,)     The  mean  solar  year  is,  365.24225  + 

J  of  (a.)  is  19.11168 

J  of  (d.)  is  19.11131 
The  variation  on  the  height  line  of  the*  king's  chamber  of 

.0128  of  a  foot,  or  of   —  of  an  inch,  affords  this  value; 

100 

that  is : 

19.0985  +  .0128  =  19.1113  feet, 

or  the  square  root  of  the  solar  year  day  value. 

(3.)  Then,  on  this  extremely  small  variation,  which  is 
within  the  limits  of  those  observed  by  Professor  Smyth, 
the  square  of  the  height  of  the  king's  chamber  equals  that 
very  quantity,  or  the  year  day  value,  of  which  its  height, 
at  its  first  intention  as  an  enlargement  on  the  standard,  af- 
fords the  subdivided  measures  on  the  celestial  circle  of 
360°.  So,  the  square  of  the  solar  year  is  involved  in  the 
miles  value  of  the  difference  of  the  earth's  diameters,  as 
connected  with  the  king's  chamber;  which,  by  one  of  its 
dimensions,  exhibits  in  the  square  root  of  that  value  a  meas- 
ure of  the  circumference  of  the  celestial  circle  of  360°. 

So,  conclusion  can  be  drawn  that  one  function  of  the 
measures  of  the  kind's  chamber  was  to  set  forth  the  cor- 
relation  of  solar  time  with  the  material  extension  of  the 
earth,  in  terms  of  the  British  inch,  foot,  or  mile. 

§  62.     (a.)     The    Hebrew  Biblical    scheme    correlates 


§62.  Sq^  Root  OF  Solar  Year  IN  King's  Chamber.    113 

strongly  with  this  :  Take  the  last  letter  of  tlie  alpliabet,  or 
iau;  its  mark  is  tiiat  of  a  cross,  or  +,  and  its  numerical 
characteristic  is  4.  The  word  Garden  0/ £^deji,  taking 
the  characteristic  values  of  its  letters,  and  adding  them, 
equals  24.  Divide  this  by  6,  and  the  result  is  4,  or  24  -^  6 
=  4.  Consider  this  as  descriptive  of  the  cross  letter,  or 
Iau — i.  e.,  that  it  represents  four  lines  in  the  form  of  a 
cross,  each  line  having  the  value  of  6.  On  this,  as  a 
frame-work,  finish  out  the  large  square,  and  there  results 
four  squares  of  6  X  6  each.  This  equals  four  areas  of  2^ 
each,  and  the  whole  equals  a  square  area  of  144,  oy  Adam, 
who  was  placed  m  the  Garden  of  Eden.  But  it  was  found, 
§  35  (3-)' that— 

(I-)  113  '  355-OOOI+  ::  36  :  113.0973, 
where  113  is  a  form  of  Adam,  in  the  word  ^' man,'^  or 
a/s/i;  from  which  form,  as  Adam  himself  says,  £^ve,  or 
t/ie  woman,  or  the  mother  of  all  living,  was  called  or 
named,  because  she  was  taken  out  of  this  form  of  113,  or 
^^man,'''  or  aish.  Instead  of  an  area  of  36,  then,  extend 
the  cross  marks,  so  that  the  four  arms  shall  represent  four 
straight  lines  of  36  each,  agreeably  with  the  value  of  36  in 
(i.),  and  perfect  the  square.  Now,  there  are  four  squares 
of  36  X  36  each,  or,  in  area,  1296  each,  or  the  numerical 
value  of  the  square  yard,  based  on  lines  of  36  in  length. 
The  four  squares,  then,  equal  1296  X  4  =  5184,  or  one 
solar  day  sign;  and,  in  fact,  the  Garden  of  Eden  is  the 
seventh  day,  thus  utilized.  The  week  of  seven  days  is  a 
circle  of  time.  Bend  them  into  the  form  of  a  circle,  and 
tiie  count  is  as  of  the  golden  candlestick  of  seven  lights, 
of  two  sets  of  three  days,  and  one  in  common,  the  phe- 
nomena when  the  cross-bars  of  the  cross  are  counted  as 
already  shown.  Each  36,  as  a  straight  line,  is  a  deriva- 
tive, as  enlargement  on  113,  or  "w«;/,"  in  (i.)  above,  as 
having  for  its  circumference  113.098-}-,  which  is  a  parallel 
use  to  that  of  the  height  of  the  king's  chamber,  for  exactly 
the  same  end  of  getting  the  use  of  the  factor  6,  except  that, 
in  this  case,  it  obtains  it  in  right  lines,  or  shifts  circular  into 
rectilinear  and  square  measure,  which  use  of  right  line  for 


114        Construction  of  the  Great  Pyramid.       §  6^. 

circular  measure  is  notoriously  true  of  the  Hebrew  Kab- 
bala. 

It  is  evident  that  the  like  uses,  and  variations,  can  be 
made  on  this,  or  the  Hebrew  form,  with  the  Egyptian. 
But,  in  fact,  it  would  rather  seem  that  both  forms  were 
made  necessary  as  developments  of  each  other. 

(d.)  The  value  of  the  word  Arels,  or  Earth,  adding 
the  characteristic  values  of  the  letters,  is  12.  It  was,  how- 
ever, the  dry,  or  arid,  or  unfruitful  earth.  To  become 
prolific  it  had  to  assume  the  Adam  form,  v/hich  it  did  by 
squaring  \\.,  or  12  X  12  =  144  =  ^^^^.  This  form  as 
144X5  =  720,  and  720X5=3600,  becomes  the  word 
Adam-h,  or  H-Adam-k,  or  ihe  fruitful  Earth,  or  the  form 
of  Mars  generator.  Here  it  can  be  seen  how  the  Garden 
of  Eden  seems  to  contain  all  the  elements  on  which  to 
frame  a  cosmogony,  by  the  help  of  other  forms  to  which  it 
is  cognate — viz.,  those  shown  as  connected  with  the  pyra- 
mid. 


SECTION  V. 

THE    BASE    OF    THE    PYRAMID. 


%6'^,     In  §  55,  in  the  diagram,  D'C  is  the  length  of  — 

side  of  base  of  the  pyramid,  taken  at  the  standard,  or 
763.4074+  feet,  divided  by  2.  The  actual  base  side  is  the 
enlargement  on  this  as  shown,  or,  763.9433+  feet,  divided 
by  2.  The  actual  construction  is  a  pavement  of  one  cubit 
in  thickness,  or,  i. 71766+  feet;  which  thickness  is  in- 
cluded in  the  height  of  the  structure.  Col.  Howard  Vyse 
places  the  base  of  the  pyramid  on  the  plane  on  which  the 
pavement  rests,  and  gives  the  thickness  of  the  pavement 

at  I  foot,  9  inches  ; 

or  in  decimals,         1.75  feet. 

As  above  1.7176+  feet. 

Difference,  -0324  of  a  foot. 


§  64.  Location,  etc.,  of  Descending  Passage- Way.  115 


SECTION  VI. 

LOCATION  AND  LENGTH  OF  DESCENDING  PASSAGE-WAY,  WITH 
RESPECT  TO  THE  INCLINED  OUTSIDE,  TO  THE  BASE,  AND  TO 
THE   VERTICAL   AXIAL   LINE   OF   THE   STRUCTURE. 

§64.     (i.;  Let  EA=the  inclined  line  of  the  sloping 


side  of  the  pyramid  from  base  to  A.     Let  E  F  =  the  — 

side  of  base.  Let  A  B  =  the  length  of  the  floor  line  of 
the  descending  passage-way,  intersecting  EA  at  A,  and 
extending  to  B,  or  to  the  foot  of  D  B.  Let  AC=  ver- 
tical height  of  A  above  E  F,  the  base  of  the  pyramid. 
And  let  D  B  ;==  the  vertical  height  of  the  base  above  the 
point  B,  or  foot  of  the  floor  line  of  the  descending  passage- 
way. The  measures  of  these  various  lines,  the  exactness 
of  which  will  be  shown  hereafter,  are  as  follows  : 

(2.)  AC  equals  31  cubits  standard,  or  51.53  feet,  plus 
the  thickness  of  the  pavement,  of  one  cubit,  or  1.71766+ 
feet,  or  a  total  of  53.24766-f-  feet,  or  638.972  inches. 
Since  the  height  to  base  side  is  as  6561  :  10306,  the  height 

to  —  base  side  is  as  6561  :  5153  ;  and  to  find  E  C  there  is 

the  proportion, 

6561  :  5153     ::     638.972  inches,  or  A  C  :  EC,  or  501. 
847693339  inches,  or  41.820641111  feet. 
Then  EC  equals,  in  length,  41.820641111  feet* 


ii6         Construction  of  the  Great  Pyramid.      §  65 


(3.)     DB  equals,  in  length,  or  height  vertical,  100  feet, 
or  1200  inches ; 

Then  AC  +  D  B  equals,  in  vertical  height,  153.2476-I- 
feet. 

(4.)     A  B  equals  200  cubits  enlarged  on  the  standard. 
The  standard  being  343-5333+  feet,  or  standard  length  of 
the  king's  chamber,  the  enlarged  value  will  be4i25.2940-f- 
inches,  or  343-7745-(-  feet. 


(5.)     To  find  CD;    AC+DB    taken  from  A  B  ,  or 


VAB    -AC  +  DB    =CD,  or  V343-7745'  -  ^SS- 
2476^  =  307.727248+  feet,  or  3692.726982+  inches. 

(6.)  EC  +  CD  =  41.820641111  -f-  307.727248  = 
349.547889  feet,  and  381.97166669  feet,  the  half  base  side 
of  the  pyramid,  less  349.547889  =  32.42377  feet,  the  dis- 
tance from  D  to  F,  the  center  of  the  structure.  The  dis- 
tance from  B  to  F'  is  the  same. 

Then,  the  distance  from  the  foot  of  the  descending 
passage-way  to  the  central  axial  line  of  the  pyramid  is 
32.42377-1-  feet. 

(7.)  With  these  data,  the  angle  AG  C,  or  that  which 
the  floor-line  of  the  descending  passage-way  makes  with 
the  base  line  of  the  pyramid,  can  be  readily  found,  as  fol- 
lows : 

Log.  A  B,  4125.29  inches,  =  3.615454 

Log.  AC  +  DB,  1838.97=  3.264576 
Sin.  90,  10.000000 

S/«.  26°  28'  24"io,  9.649122 

(§  65.)  It  is  well  enough  to  give  the  measures  and  data 
for  measures,  from  Col.  Howard  Vyse  and  Professor 
Smyth.  Col.  Vyse  excavated  the  rubbish  heap  laying  over 
E  A,  and,  at  the  foot,  took  the  measures  of  the  pavement 
as  to  its  thickness,  which  he  calculates  in  the  measures  of 
the  mass.  At  E,  he  found  a  casing-stone  in  place,  which 
gave  him  the  position  of  E  and  the  line  EA.  The  floor 
line  of  the  passage  way  terminates  in  a  broken  edge,  which, 
measuring  from  E,  for  perpendicular  height,  he  gives  at 
49  feet  above  the  bottom  of  the  pavement.  Continuing 
from  this  edge,  downward,  162.3  inches  (Professor  Smyth's 


§  65.  Location,  etc.,  of  Descending  Passage-Way.  117 

measure,  who  says:  "From  the  beginning  of  the  roof 
dropped  onto  the  floor  Hne  to  the  edge  of  basement  sheet 
is  162.3  inclies"),  along  the  floor  line,  brings  one  to  the 
place  where  the  roof  of  the  passage-way  commences,  in 
the,  at  present,  broken  masses  of  masonry.  Thence,  Col. 
Vyse  measured  down  3850  inches.  As  to  this  last  dis- 
tance, he  says  :  "  Or  present  length  inclined  of  whole  en- 
trance passage,  3850  inches.  But  ancient  length  must  be 
increased  for  an  extent  of  more  than  276  inches  broken 
away  at  the  beginning,  with  the  exterior  of  the  building, 
and  is  therefore  more  nearly  4126  inches."  That  is,  his 
estimate  of  the  restored  distance  A  B  is  4126  inches.  The 
measure  here  taken  is  4125.294  inches,  differing  from  his 

7 
estimate  by  the  amount  of  .706,  or  — -of  one  inch,  in  that 

many  thousands  of  inches. 

He  gives  the  angle  of  the  casing-stone  found  as  51°  50' 

He  gives  the  angle  A  G  C  (§  64)  as  26°  41' 

(§  66.)     Following   down   the    lead   of  the    descending 

passage-way,  he  gives  the  distance  A  D  to  the  subterranean 

chamber,  at  27   feet ;    for  he   measured   along   the    roof 

line,  not  the  bottom  line.     He  does  not  give  the  distance 

B  E,  but  on  Perring's   plates  of  Vyse's    measures,  which 

are  very  faithfully  done,  while    A  D    shows    as    27   feet, 


JE 


J" 


B  E  shows  as  29  feet,  which  goes  to  confirm  the  opinion 
that  the  line  G  B  is  parallel  to  the  exterior  inclined  line  of 
the  pyramid.  The  height  of  A  C  he  gives  at  three  (3)  feet. 
Taking  Col.  Vyse's  data  just  as  he  gives  them,  and  for 
B  F,  that  is,  from  the  foot  of  the  descending  passage-way 
to  the  center  of  the  pyramid,  the  values  are — 


ii8        Construction  of  the  Great  Pyramid.      §  66. 


BtoC  — 

2.358-1-       feet 

C  toE  = 

27.000           " 

EtoF  — 

3.56899+    " 

Or  a  total  of  32.92699  " 
While  this  is  so,  /ic  says  that  F,  instead  of  3.568+  feet,  is 
distant  from  E  8  feet — a  manifestly  erroneous  calculation, 
from  his  ow7i  data.  The  difference  between  the  results  of 
calculation  from  the  data  of  Col.  Vyse,  and  from  those 
stated  for  this  distance,  is  as  follows  : 

Col.  Vyse's  estimate,  32.92699  feet. 

As  given  above,  32.42377 


( ( 


(< 


Difference,  -50322 

and  this  is  to  be  accounted  for  by  the  difference  of  the  an- 
gles taken,  his  being  stated  at  26°  41' 
while  that  resulting  from  the  data  herein 

taken  is  26°  28'  24^10. 

There  is  very  strong  confirmation  as  to  the  correctness 
of  this  last  stated  angle.  Without  any  certain  data  to  go 
by,  the  only  method  of  obtaining  the  relations  between  the 
interior  and  exterior  lines  of  the  structure,  was  by  means 
of  this  angle  ;  and  therefore  it  was  of  the  greatest  impor- 
tance to  obtain  it  correctly.  Aware  of  this,  Professor 
Smyth  prepared  for  its  determination  to  within  very  close 
limits.  He  found  a  material  difference  between  the  real 
angle,  and  that  as  stated  by  Col.  Vyse,  of  26°  41'.  He 
used  three  different  instruments,  and  made  a  number  of 
separate  trials  for  each  instrument ;  and  his  determinations 
may  be  looked  on  as,  for  the  condition  of  the  passage  it- 
self, as  close  an  approximate  as  may  be  expected  to  the 
true  angle — the  correction  being  the  obtaining  those  orig- 
inal elements  of  construction,  which  gave  rise  to  this  angle. 
His  results  are  as  follows : 

(i.)     By  one      method,      26°  27'  >  .„     ,, 

CO    ^,.        \  mean,  26°  26^5 
26    26'5        5 

(2.)     By  another      "  26°  25'  20"         "      26°  25'  20" 

(3.)     By  another       "  26°  27' 58"  ^       ^^ 

26°  28'  16"  \  20    -o     7 


§  67-  Location,  etc.,  of  Descending  Passage- Way.  119 

The  admeasurements  used  to  obtain   these   means  are 
themselves   the   means  of  measures,   some  of  which   ex- 
ceeded that  angle  here  used.     Professor  Smyth  while  aver- 
ring that  the  true  angle  is  very  closely  connected  with   the 
results  given  by  him,  lays  no  stress  upon  any  particular  set, 
considering  them  all  as  equally  worthy.     But  compare  one 
set  of  his  with  that  angle  resulting  from  the  data  herein 
used  for  locating  the  floor  of  the  passage-way  : 
(4.)     Professor  Smyth's,  26°  28'     7" 
(5.)     That  stated  above,  26°  28'  24"io 
showing  a  difference  exceedingly  small,  as  may  be  realized 
if  one  will  try  to  read  it  on  the  face  of  an  instrument. 

§  67.      The   genius  of    the  pyramid  demands  that  the 
angle  of  the  side  incline  be,  51°  51'  !/{"<, 

Col.  Vyse  got  by  the  measure  of  one  stone,  51°  50' 
Compare  these,  and  then  the  agreement  of  the  angles, 

26°  28'  24"  10 
26°  28'    7", 
then  the  restored  length  of  the  descending  passage-way  by 
Col.  Vyse  of  4126  inches, 

with  that  above  of  4x2=^.294       " 
then  the  restored  height  of  the  intersection  of  the  floor  line 
of  the  passage-way  with  the  slope  exterior  line,  as  made 
by  Vyse  with  his  own  angle  of  26°  41',  53-648-!-  feet, 
and  with  the  angle  of  Smyth,  say,  53-1975      " 

and  that  above,  53.2476      " 

Consider  with  these  data  that  the  measures  here  obtained 
ire  from  use  of  the  Parker  measures  of  the  -pyramid^  har- 
nonizing  with  the  general  measures  of  the  mass,  and  of 
he  king's  ehamber ;  and  there  is  needed  hut  slight  confirni- 
itory  evidenee  that  the  general  data  taken  are  the  original 
and  veritable  ones  used. 

§  68.  There  is  another  numerical  value,  having  an  ele- 
mental value,  closely  related  to  that  of  A  C,  in  §  64  (2.) — 
viz.,  53.05162,  say,  feet  =  636.61944498  inches  ;  as  to  which 
something  is  to  be  said  in  the  way  of  its  application  to  the 
vertical  height  of  the  descending  passage-way,  as  an  inch 
value — viz.,  53.05-f-  inches,  to  the  breadth   of  the   same, 


I20        Construction  of  the  Great  Pyramid.      §  69. 

and  to  its  height  perpendicular  to  the  floor  line  ;  of  which 
hereafter.  The  half  of  636. 6i94-f->  or  318.309722-I-  inches, 
is  a  diameter  value  to  a  circumference  of  1000.  This  is 
more  noticeable  since  100,  the  height  in  feet  of  B  D,  is  a 
circumference  to  a  diameter  value  of  31.830972-}-,  and 
31.8309724-  X  12  =  381.9716-1-,  or  the  value  of  the  half 
base  side  of  the  pyramid  in  feet,  which  is  a  diameter  value  to 
a  circumference  of  1200.  Somewhat  in  this  connection,  the 
length  of  the  line  A  B  of  343.7745-}-  is  just  equal  to  10 
times  the  length  of  the  actual  measure  of  the  king's  cham- 
ber, or  an  enlargement  on  the  standard  of  34-3533-}—  The 
number  343-7745-}-  ^^  a  diameter  value  to  a  circumference 
of  loSo.  Taking  this  as  feet,  then,  reduced  to  inches,  or 
4125-}-,  it  becomes  a  diameter  value  to  a  circumference  of 
12960  inches,  which  number  1296  is  the  number  of  square 
inches  to  the  square  yard  British. 

§  69.  There  is  something  strongly  confirmatory  as  to 
the  location  and  lenfjth  of  the  floor  line  of  the  descendinrr 
passage-way,  as  given,  if  there  are  showings  to  confirm  the 
fact  of  the  distance  from  the  foot  of  that  passage  to  the 
central  axial  line  of  the  mass,  being,  as  taken,  32.42377+ 
feet. 

(i.)  One  justification  of  this  is  in  its  connected  use 
with  the  length  of  the  top  line  of  the  horizontal  subterra- 
nean passage-way  to  the  subterranean  chamber.  Now,  the 
above  length  can  be  taken  at  324.2377+  tenths  of  feet ; 
the  length  of  the  said  top  line  is  given  by  Col.  Howard 
Vyse  at  27  feet.  This,  in  inches,  is  324.  So  that,  by 
comparison,  the  distance  along  the  top  line  to  the  subter- 
ranean chamber  is  324  inches  ;  the  distance  along  the  bot- 
tom line  to  the  central  vertical  axial  line  of  the  entire 
mass  is  324  tenths  of  feet.  The  variation  from  the  exacti- 
tude of  comparison  is  .0198  of  a  foot  (for  27.0198  feet  X  12 
=  324.2376  inches) — an  amount  so  small  that  it  may  be  that 
this  was  or  is  included  or  embraced  in  the  measure  of  the 
top  line.  Right  here,  too,  it  will  be  remarked,  by  refer- 
ence to  the  table  §  53  (<5.),  that  324  is  a  circumference  to  a 
diameter  of  103.132  +  ,  which,  in  inches,  is  the  half  width 


§  69.  Location,  etc.,  of  Descending  Passage-Way.  121 

of  the  king's  chamber,  as  enlarged  on  the  standard,  or  the 
enlargement  of  5  cubits;  as,  likewise  in  §  55  («.),  it  is 
seen  to  be  circumference  to  the  base  of  the  ideal  p3''ramid 
placed  in  the  sphere  (enlargement  on  the  standard  being 
made). 

(2.)  There  is  another  harmonic  relation,  which  seems 
to  place  the  location  of  these  lines  and  limits  beyond  ques- 
tion, and  thus  to  close  these  lines  as  located.  The  bare 
showing  of  the  relations  serves  to  confirm  the  purposed  use. 


The  floor  line  of  the  descending  passage-way,  as  shown, 
from  A  to  B,  has  been  stated  to  be        343-7745+  feet. 
From  B  to  C,  the  vertical  axial  line  is  32.4237+     " 

It  seems  evident  that  the  use  of  343-7745  is  a  use  in  con- 
nection with  the  half  base  side  of  the  pyramid  enlarged, 
or  381.97166-I-  feet, 

as  shown  in  §  64  (6),  and  §  70. 

With  B  C,  find  the  length  of  B  D,  or  A  B  protracted  to  D, 
the  vertical  axial  line  of  the  pyramid ;  then  B  D  = 

36.22189  feet. 
Now,  if  the  value  381.97166-I-  is  in  contemplation  in  the 
use  of  this  floor  line,  add  A  B  and  B  D  together,  to  see 
what  is  wanting  to  make  up  the  distance  381.97166  + 

and  so—  (i.)     343.77450 

36.22189 
1.97527 
381.97166 

The  deficit  is  seen  to  be  1.97527  feet. 

But,  instead  of  summing  up  the  total  lengths^  take  the  line 
B  D  alone,  which  is  the  hypothenuse  to  the  distance  B  C, 


122        Construction  of  the  Great  Pyramid.      §  70. 


or  the  measure  32.4237+  feet  in  question,  and  to  it  add 
the  surplus  required,  or  deficiency,  1.97527 — 

(2.)     36.22189+ 

1-97527+ 

38.19716+ 
and  here,  numerically,  is  the  same  value  as  obtained  by 
adding  the  totals.  Here,  38.19716+  feet  is  obtained,  which  is 

just  the —  part  of  381.9716+  feet.     The  harmony  is  such 

that  it  is  thus  deemed  conclusive  that  the  floor  line  of  the 
descending  passage-way,  as  to  length,  and  as  to  its  location 
relatively  to  the  exterior  slope  line  and  to  the  vertical  axial 
line  of  the  structure,  has  been  taken  agreeably  to  the  men- 
tal conception  of  the  architect.  In  the  final  closing  of  the 
lines  of  the  interior  works,  this,  it  is  thought,  will  be  con- 
firmed. 

§  70.  A^ote  to  above.  The  distance  from  the  foot  of  the  de- 
scending passage-way  floor  to  the  center  of  the  pyramid,  is  stated 
at,  numerically,  3242377-f-.  There  are  very  strong  reasons  in  the 
harmony  of  relations^  goi^g  to  show  that  this  is  the  exactitude 
intended  ;  indeed,  it  seems  to  force  conviction  to  that  effect  upon 
the  mind.  Whatever  other  uses,  or  interpretations,  may  have 
been  ascribed  to  the  pyramid  numbers,  there  certainly  seems  to 
have  been  a  wonderful  play  upon  them.  Take  381.97166+  ;  the 
half  base  side  of  the  pyramid  ;  deduct  from  it  the  length  of  the 
floor  line  of  the  descending  passage-way — viz.,  343-7745+  '  ^"^ 
the  remainder  is  38.197166+,  simply  showing  that  this  floor  line 

is  iust  the  value  of  half  base  side  less  one-tenth. — ,  of  itself.    If 
•'  10 

from  E,  §  64  (i.),  343.77+  be  measured  toward  the  center  of  the 
pyramid,  there  will  remain  next  to  the  center  a  distance  of 
38. 1 97 1 66+ feet.  Besides  this,  this  343.77+  is  just  ten  (10)  times 
the  numerical  length  of  the  king's  chamber ;  and  in  this  connec- 
tion, especially  for  the  purpose  in  hand,  the  height  of  the  king's 
chamber  is  another  play  upon  this  value — viz.,  19.09S5S3+  feet. 

But  to  the  present  purpose  of  showing  some  possible  uses  of 
334237+,  which  may  help  others  in  this  study- 

(a.)  Construct  a  pyramid  out  of  the  original  Parker  elements, 
which  shall  be  in  the  proportions  of  the  one  in  question  :  the 
height  will  be  6561,  and  the  base  side  will  be  5153  X  3  =1^  10306. 


§  70-  Location,  etc.,  of  Descending  Passage-Way.  123 


If  this  pyiamitl  be  placed  in  a  sphere^  the  axial  line  of  the  pyr- 
amid— that  is,  its  vertical  axial  line,  or  6561 — to  become  the  radius 
of  such  a  sphere  must  be  extended  until  its  length  becomes 
7337.658816-}-.  If  this  value  be  divided  by  20612,  the  quotient 
will  be  355-50454-.  7327.-}-  being  in  inches,  divided  by  20.612, 
the  quotient,  or  355.-|-,  is  in  the  value  of  cubits.  Take  the  height 
of  the  king's  chamber,  and  to  its  numerical  value  add  this  quo- 
tient as  follows : 

1909S5S3+ 
355504+ 

194540S7 
Divide  this  sum  by  6  and  the  quotient  will  be  3242347-}-. 

((5.)     But,  again,  the  enlargement,  so  much  used  throughout 
the  pyramid  works,  on   the  cubit   standard  value,  in  inches  of 

20.612  is  20626.47001 7-}-.       This   X — =  330023.520272;  and 

this  divided  by  20.612=  1779. 024S,  as  the  enlargement  of  the 
standard  cubit  value  of  the  circumference  of  the  pyramid — viz., 

i777-777~f~-     One-fifth  j  —  j   of  this  enlarged  value  355.8049,  is 

the  enlargement  on  the  corresponding  division  of  i777"4"  divided 
b}'-  5,  or  355-555-}-.  Now  take,  again,  the  numerical  value  of 
height  of  king's  chamber,  and  add  this  enlarged  cubit  value  to 
it—  1909S583 

3558049 

194543S79; 
and  the  one-sixth  (  ^  )  of  this  is  32423979. 

(c.)     Take  the  mean  of  the  resultant  values  in  (a.)  and  ((5.)  : 

32423979 

3242347 

2  I  64S47449 
3242372-f-. 
Compare  with  this  the  numerical  value  of  the  distance  from  B  in 
§  (>6^  to  F,  or   32.42377-}-  feet.      The  difierence    seems   to   be 
5  I  1 00000  of  a  foot. 

On  the  face  of  the  workings  of  the  numbers,  with  their  seen 
relations — viz.,  (i.)  to  the  value  of  the  circumference  of  the  pyr- 
amid, and  (2.)  to  the  extension  of  the  axial  line  of  the  same  to 
obtain  the  radius  of  its  containing  sphere,  and  (3.)  to  this  shown 
o  be  related  number  down  in  the  subterranean,  as  it  were  toward 


124        Construction  of  the  Great  Pyramid.      §  71. 

the  center  of  this  sphere :  add  to  these  the  general  marvelous  ac 
curacy  of  adjustment  of  the  various  measures  through  which  thia 
measure  is  attained,  with  the  best  measures  of  these  various  pai'ts 
with  the  angles  of  direction  ;  and,  again,  that  these  are  every  one 
of  them  Parker  and  pyramid  elements.  This  done,  the  effect  on 
the  mind  is  strong  that  the  measures  taken,  with  their  uses  as 
shown,  determine  the  location  of  the  central  axial  line  of  the 
pyramid,  agreeably  to  the  mental  conception  of  the  architect.  It 
must  be  observed,  however,  that  this  very  number  may  have  va- 
rious uses,  agreeably  to  the  wonderful  interplay  of  these  pyra- 
mid numbers  at  every  turn. 

One  thing  further  is  worthy  of  consideration — viz.,  the  differ- 
ent lengths  of  lines,  or  measures,  of  rooms,  passage-ways,  coffer, 
and,  by  inference,  of  the  whole  mass  of  the  pyramid,  raising  a 
system  of  variations,  very  minute  it  is  true,  but  nevertheless, 
pointing  to  a  system  of  recognition  of  variations  on  some  stand- 
ard or  standards.  Agreeably  to  this,  all  the  above  results  might 
have  been  in  contemplation,  as  the  difference,  or  variation,  be- 
tween 32.42347,  32.42397,  and  32.42377  could  not  possibly  be 
given  in  any  mechanical  work  ;  for  the  differences  .00047,  00097, 
and  00077  ^^  ^  ^'^^^  ^^'^  inappreciable. 


SECTION  VII. 


THE  DESCENDING  PASSAGE-WAY  IS  SET  OFF  TO  THE  EASTWARD 
OF  THE  VERTICAL  AXIAL  LINE  OF  THE  PYRAMID  A  DISTANCE 
OF    24.42190    FEET. 

(§  71.)  The  mouth  or  entrance  of  the  descending 
passage-way  is  upon  the  north  face  of  the  mass  ;  and  while 
its  end  or  foot  terminates  at  a  distance  of  32.44-  feet  to  the 
north  of  the  center,  the  whole  passage  is  set  off  to  the 
eastward  of  the  same  center.  Agreeably  to  the  estimates 
of  Col.  Vyse,  this  descending  passage-way,  as  to  the  cen- 
ter longitudinal  line  of  its  floor,  is  set  off  from  the  vertical 
axial  line  of  the  pyramid  a  distance  of  294  inches,  or  24.5 
feet.  Col.  Vyse  must  have  taken  this  measure  of  24.5 
feet  relatively  to  his  estimate  of  the  length  of  the  side  of 


§  7i«  Descending  Passage  to  one  Side  of  Center.  125 

the  base,  which  was  764  feet.  Corrected  at  763.9432+ 
feet,  which  is  supposed  ta  be  the  exact  measure  intended, 
works  a  correction  on  24.5  feet,  as  follows:  382  —  381.- 
p7i66  =  .0284,  to  be  deducted  from  24.5  feet,  leaving,  as 
the  corrected  distance,  as  Col.  Vyse  must  have  made  it, 
had  he  used  these  data,  the  sum  of  24.4716+  feet. 

It  appears  that  the  passage-way  was  set  off  to  about  this 
distance,  as  designative  of  the  final  difference  of  216330, 
obtained  by  placing  the  pyramid  in  its  standard  dimensions 
in  a  sphere,  as  already  set  forth.  As  this  number  has  been 
shown  to  be  instrumental  in  giving  one  value,  toward  the 
center,  of  32.42347,  so  it  appears,  likewise,  by  use  of  the 
same  numerals,  but  under  another  form,  to  fasten  the  loca- 
tion of  the  other  distance  from  the  center. 

(a.)  The  radius  of  the  sphere  in  which  the  pyramid 
was  placed  was  shown  to  be  7327.6588172+,  which,  re- 
duced to  feet,  is  610.63S23  +  .  From  7327.6588172+,  there 
was  taken  the  difference  of  216330,  as  an  elliptical  prop 
erty.  It  seems  that  this  number,  as  such,  was  preserved 
intact  (on  different  scales  of  measure),  and  was  deducted 
from  610.  +  as  follows  : 

(i.)     610.63823  —  .216330  —  610.42190  feet, 
leaving  a  base  of  calculation  regulating  several  governing 
measures  of  the  interior  works. 

(p.)  Let  the  pyramid  inclosed  in  a  sphere  be  taken  at 
the  standard  height — viz.,  486  feet.  Add  to  this  the  depth 
of  the  floor  of  the  subterranean  passage-way  of  100  feet, 
below  the  base  of  the  pyramid.  The  sum  will  be  586  feet. 
Let  it  be  taken  that  the  intention  was  to  use  these  values  so 
that  a  mark  would  exist  in  the  works,  that  this  process  had 
been  gone  through  (a.)  (i.)  From  the  610.42190  feet 
take  the  586  and  it  will  show  the  distance  from  the  top  of 
the  pyramid,  taken  from  the  radius  of  the  circle,  less  the 
amount  of  the  ellipticity  shown,  or  216330,  thus  : 

(i.)     610.63823  —  586  +  .216330=  24.42190  feet. 
Thus  showing  the  bottom  of  the  subterranean  passage-way 
to  be  above  the  true  center  of  the  sphere  a  distance  of 
(2.)     24.42190+  ,216330  =  24.63823  feet. 


126         Construction  of  the  Great  Pyramid.      §  72. 

(c.)  From  the  center  axial  line  set  the  central  longitudi- 
nal line  of  the  passage-way  off  this  distance  of  24.42190 
feet,  as  indicating  the  above  process,  and  let  this  be  the 
fixed  limit  line  for  the  interior  works.  By  Col.  Vyse's 
measures  as  corrected,  this  limit  line  is  shown  to  be  fixed 
at  24.47 i-j-  feet  from  this  axial  line.     By  comparison,  then, 

Col.  Vyse's  distance,  24.471-I- 

By  above,  24.4219 


Difference,  .0491 

6 

or  —  of  one  inch  ;  an  amount  to  be  allowed  as  his  error  of 
10 

measure,  provided  the  assuming  the  above  distance  be  sup- 
ported as  correct  by  other  showings,  in  related  measures. 

While,  therefore,  the  foot  of  the  descending  passage-way 
has  been  shown  to  be  distant  from  the  vertical  axial  line  of 
the  pyramid,  to  the  northward  32.42347-j-  feet,  the  same, 
from  calculations  growing  out  of  the  like  governing  data, 
is  assumed  to  be  set  off  to  the  eastward  of  the  same  axial 
line 

24.42190-f-  feet, 
as  indicating  the  geometrical  conditions,  or  relations,  made 
by  placing  the  pyramid  in  a  sphere ;  modified   by  the  re- 
jection of  the  value  .216330. 


SECTION  VIII. 
THE    DIMENSIONS   OF   THE    DESCENDING   PASSAGE-WAY. 

§  72.  The  question  as  to  the  dimensions  of  the  descending 
passage-way  may  now  be  taken  up.  It  has  been  seen  that 
all  the  measures  of  the  structure  have  their  origin  in  the 
relation  of  circumference  and  diameter  values  of  a  circle 
It  would  be  exceedingly  appropriate  that  in  the  act  of  en- 
tering the  passage-way,  one  should,  as  a  matter  of  fact, 
enter  through  the  actual  expression  of  those  values.  Such 
seems  to  have  been  the  case. 


§  72.     Dimensions  of  Descending  Passage-Way.       127 

Col.  Vyse's  measures  of  this  passage  are  : 
(i.)     Breadth,  41.5 

Height  perpendicular  to  incline,  47.0 
Professor  Smyth's   measures   are   grouped  together,  as 
means  of  a  series,  and  are  as  follows  : 

(2.)     Breadth  near  bottom,  41.61  to  41.46  inches. 
"       top,         41.63  to  41.41       " 
Mean  of  all,  ^^-53       *' 

(3.)     Height  perpendicular  to  incline  : 

West  side  of  floor,  47.16  to  47.30  inches. 
East  side  of  floor,  47.14  to  47.32       " 
Mean  of  all,  47-24       " 

But  he  characterizes  this  measure  as  47.3  inches. 
(4.)     Height  vertical  to  base  of  pyramid  : 
In  one  place,  52.68  inches. 

In  another       "       52.36        " 
There  seems  to  be  very  little,  if  any,  difference  between 
the  dimensions  of  the  descending,  and  of  the  ascending, 
passage-way  ;    and,   as  the  red   granite   portcullis  blocks 
seem  to  have  been  intended  to  give  these   measures,  it  is 
well  to  give  Professor  Smyth's  measures  of  the  same — viz  : 
(5.)     Height  perpendicular  to  incline,         47.3  inches. 
Breadth,  41.6      " 

Height  vertical  to  base  of  pyramid,  53.0  " 
[a.)  In  §  64,  the  point  A  being  the  intersection  of  the 
floor  line  of  the  descending  passage-way,  is  in  vertical 
height  above  C,  31  cubits,  or  53.24766+  feet;  while  E  C  is 
41.82064  feet.  Attention  was  called  to  a  numerical  value 
very  near  to  this  height  line — viz.,  53.05162,  say,  feet. 
Had  the  value  been  this  last  one,  its  meaning  would  have 
been  a  very  peculiar  one,  for,  in  inches,  it  is  636. 61944 -f, 
and  the  half  of  this  is,  numerically,  3 18309+ ,  or  the  value 
of  diameter  to  a  circumference  of  unity ^  or  one. 

Take  the  proportion  (see  diagram,  §  64)  : 
(i.)     (AC  :  EC),  or  53.2476  :  41.8206     ::     53.05162  : 

41.6666+  ; 
and  here  in  the  last  terms  are  to  be  found  the  vertical 
height,  and  the  breadth  of  the  portcullis  blocks,  (5.)  above, 


128        Construction  of  the  Great  Pyramid.      §72. 

as  given  by  Professor  Smyth,  in  the  scale  o{  an  inch  to  the 
foot;  and  a  minute  change  upon  the  dimensions  of  the  de- 
scending passage-way,  as  given  by  him. 

It  must  be  noticed  that  the  vertical  height  of  the  passage 
is  simply  dependent  on  the  accident  of  its  angle  of  eleva- 
tion, and  that  angle  being  26°  28'  24"  10,  for  a  vertical 
height  of  53. 05162,  the  height  of  the  passage  perpendicular 
to  the  incline  must  be  47.48771-]-  inches,  instead  of  47.16 
or  47.32,  the  extremes  given  by  Professor  Smyth;  show- 

16 
ingf  thus  a  difference  of    —  of  an  inch  on  his  extreme. 
^  100 

(3.)  If  it  is  as  stated  by  Professor  Smyth,  that  there  is 
throughout  the  works  the  exhibition  of  two  sets  of  meas- 
ures throufih  biased  lines,  let  it  be  taken  that  while  there 
is  in  the  dimensions  of  this  passage-way  the  relation  of 
circumference  of  07ie  to  its  diameter,  as  seen,  it  was  in- 
tended to  display  the  reverse  relation,  also,  of  circumfer- 
ence to  a  diameter  of  one,  then  : 

(!•)     314159+  X  2  =  6283184  -M2  =  52.3598-f  feet. 
And,  carrying  out  the  proportions — 

(2.)  53-05i6-f  :  47.48778+  ::  52-3598+  •  46.8684+; 
in  which  the  last  term  is  the  height  perpendicular  to  the 
incline. 

(c.)     Suppose  both  of  these  measures  to  have  been  in- 
ferred bv  the  exhibition  of  their  mean  values,  then  there 
results  the  use  of  two  sets  of  measures,  as  follows  : 
(I.)     Height  vertical,  53-05i62      52.3598 

Height  perpendicular  to  incline,  47.4S778      46.868 
Breadth,  41.66  41. i 

of  which  the  mean  would  be — 

(2.)      Height  vertical,  52.7057  inches. 

Height  perpendicular  to  incline,  47.1778       " 
Breadth,  4^^-39  " 

The  measures  of  Professor  Smyth  give  like  values,  as — 
(3.)      Height  vertical,  52.68  to  52.36 

Height  perpendicular  to  incline,  47.16  to  47-32 
Breadth,  41-41  to  41.61 

where,  in  52.68,  47.16,  and  41.41,  this  set  of  mean  values. 


§  72.    Dimensions  of  Descending  Passage-Way.      129 

had  it  been  intended,  would  hardly  have  been  more  nearly- 
measured  than  thus  shown.  It  is  worthy  of  notice,  too, 
that  the  portcullis  blocks  are  in  the  color  of  the  king's 
chamber,  which,  in  its  height,  is  a  diameter  to  a  circum- 
ference of  60,  the  base  of  360°,  or  time  measure.  Now,  the 
measures  of  these  blocks,  as  given,  denote,  in  53.0,  the  re- 
lation of  diameter  to  a  circumference  of  U7iity — the  very 
change  on  which  the  king's  chamber  height  is  founded. 

There  is  much  to  be  said  in  favor  of  these  results.  They 
grow  out  of  each  other,  and  are  proportional  to  the  pyra- 
mid relations  A  C  :  C  E.  In  doing  so,  they  involve  three 
relations  of  dimensions  in  this  passage-way,  and  develop  each 
relation ,  as  it  has  reference  to  the  actually  measured  one,  with 
the  accuracy  seen.  Besides,  the  germ  of  the  measures  is 
in  perfect  harmony  with  the  use  of  all  the  measures  used 
in  and  about  the  structure  ;  and  gives  the  unit  values  of  di- 
ameter and  circumference  of  i  :  314159,  and  of  I  :  318309 
as  relations,  which,  for  extended  cosmical  uses,  are  used 
in  the  integral  forms,  6561    :    20612,  and  113   :    355. 

{d.)  There  is  a  very  strange  coincident,  and  real  natu- 
ral relation,  which  goes  very  far  to  support,  not  only  what 
has  been  said,  but  serves  to  strengthen  the  general  scheme 
as  to  the  use  of  the  pyramid  measures,  as  co-ordinating 
thne  and  distance  \2X\xq?..  This  53.05126+  feet,  or  6'^6.' 
61944+  inches,  shows  the  relation  of — 

(i.)  636.61944  ^  2  =  318.309+, 
or  of  diameter  to  circumference  of  1000,  or  of  one.  Take 
the  received  value  of  the  earth's  equatorial  diameter  in 
miles,  or  7926.6789+  miles.  Square  this  value,  and  there 
results  62832238.3837+  miles  in  area.  Divide  this,  as  in 
(I.)  above,  and  there  results — 

(2.)     62832238-^-2  =  3x416119. 

Compare  this  result  with  the  relation  of  circumference  to 
a  diameter  of  unity  as  an  abstract  one — 

(3.)     3141611  —  3141594  =  0.000017, 
and  this  shows  an  amazing  relation  between  the  square  of 
the  earth's  equatorial  diameter  in  miles  and  the  abstract  re- 
lation of  diameter  of  unity  to  its  circumference,  the  exacti- 


130         Construction  of  the  Great  Pyramid.      §  72 

tude  being  included  in  the  variation  of  the  measure  of  this 
passage,  or  between  its  limits.  Take  it  the  other  way, 
with  Parker's  ratio  of  circumference  to  diameter  of  unity, 
and  V31415942  X  2  =  7926.565  +  .  While  this  is  so,  as 
has  been  seen,  the  other  relation  of  circumference  as  one  to 
d'lameter  as  318309  was  made  use  of  to  raise  from  6  the 
value  360°,  or  the  measure,  geographically,  of  this  self- 
same equatorial,  as  to  its  circumference,  to  make  it  co- 
ordinate with  solar  time  value  on  the  celestial  circle  of  360°. 
So,  it  thus  seems  that  the  above  processes  were  likely  used 
as  recognizing  and  making  practical  use  of  these  relations. 

On  assumption,  then,  with  this  showing,  the  measures  of 
this  passage-way  are  takenyi?r  a  mean  value  of,  for 
Height  vertical,  52.7058  inches. 

Height  perpendicular  to  incline,   47.1778       " 
Breadth,  41.39  *' 

and  it  will  be  seen  that  this  intention  was  carried  out. 

(e.)  It  is  necessary  to  obtain  some  of  the  above  dimen- 
sions before  one  can  make  any  study  of  the  works  con- 
nected with  the  ascending  passage-way,  as  to  their  relations 
to  the  descending  passage-way,  and  to  the  mass  of  the 
pyramid. 

The  fact  of  the  dimensions  of  the  descending  passage-way  be- 
ing constructed  on  biased  lines,  the  mean  of  which  are  given 
above,  might  be  accompanied  by  a  biased  condition  of  the  as- 
cending passage-way  ;  so  that  a  choice  as  to  elevation  of  the  foot 
of  the  ascending  passage-way,  could  be  made  between  the  ex- 
tremes of  46.868  and  47.4876,  the  mean  being,  as  has  been  stated, 
47.1778. 


For  connection  of  the  upper  works,  the  perpendicular 


§  73*   The  Location  of  Ascending  Passage- Way.    131 

AC,  from  the  roof  end  of  the  descending  passage-way  to 
the  floor  of  the  horizontal  passage-way  to  the  subterranean 
chamber  must  be  had  in  its  measures.     Let  the  values  of 
the  lines  in  the  diagram  be  as  follows  : 
(i.)     B  D,  Height  perpend,  to  incline,     47.30836  inches. 
(2.)     AB,  parallel  to  slope  lineof  pyr.,  48.30736       " 
(3.)     AC,  perpend,  to  horizon,  passage  37.9908         " 
A  reason  for  this  becomes  manifest.     Take  the   two   rela- 
tions of  diameter  of  i  to  a  circumference   of  314159,  and 
circumference  of  i,  to  a  diameter  of  318309.     Their  sum 
is  632468,  and  their  mean  value  will  be 

316238. 
37.9908  inches,  -4-  12  =  3.16590,  showing  a  difference  of 
.00352   of  a   foot,  to  verify  all  that  has  been   said.     The 
use  then  is  the  mean  of  the  abstract  values  stated  X  by  12. 


SECTION  IX. 

LOCATION  OF  INTERSECTION  OF  FLOOR  LINE  OF  ASCENDING 
PASSAGE-WAY,  WITH  THE  ROOF  LINE  OF  DESCENDING  PAS- 
SAGE. 

§  73.  The  dimensions  of  the  descending  passage-way 
give  the  juean  measures, 

Height  vertical,  52.7058  inches. 

Height  perpendicular  to  incline,  47-178         " 
A  variation  on  the  last  of  these  measures,  to  locate  the  as- 
cending passage  way,  is  taken  at 

Height  perpendicular  to  incline,  47.3083  inches. 
(Professor  Smyth's  measure,  47.3000)     " 

Having  these  data,  the  next  step  in  order  is  to  ascertain 
the  point  of  intersection  of  the  floor  line  of  the  ascending 
with  the  roof  line  of  the  descending  passage-way. 

[a.)  The  author  found  a  point  in  common  between  the 
measures  of  Colonel  Vyse  and  Professor  Smyth  of  the  de- 


132         Construction  of  the  Great  Pyramid.       §  73. 

scending  passage-way  ;  which  point  turns  out  to  be  of  im- 
portance as  to  the  location  of  the  ascending  passage-way. 
Colonel  Vyse  commenced  his  measures  from  B,  giving 
the  total  length  B  D  at  3850  inches.     (The  edge  of  the 


roof  stone  B,  is  a  broken  and  an  uneven  edge,  and  for  a 
finish  may  have  projected  beyond  its  present  face).  From 
B,  he  says,  to  the  junction  of  the  first  ascending  passage- 
way is  758  inches.  Professor  Smyth  measuring  from  A, 
gives  AB'  at  162.3  inches,  then  from  A' to  C,  that  is, 
"  from  basement  beginning  to  joint  18  situated  up  in  a  hole 
which  is  the  continuation  of  portcullis  blocks,"  (or  of  the 
upper  line  of  the  ascending  passage-way),  "  of  first  as- 
cending passage-way,  and  in  their  inclined  line,"  981.9 
inches.  C  is  at  this  point,  or  joint.  Then  from  B  to  C' 
by  Mr.  Smyth,  is  981.9  —  162.3  —  819.6  inches.  He  gives 
the  distance  from  O,  or  joint  17,  to  C  as  60.0  to  60.3, 
inches  ;  then  from  B  to  O  is  819.6  —  60.2  =  759.4  inches. 
Take  it  so,  759.4  inches. 
It  is  to  be  seen  that  the  point  O  is  at  the  junction,  and 
Colonel  Vyse  says  it  is  distant  from  B,  758  inches.  This 
seems  to  raise  a  common  objective  point  of  measure  for 
these  gentlemen,  with  a  difference  of  759.4 —  75S  =  1.4 
inches  ;  which  perhaps  may  be  accounted  for  in  their  points 
of  beginning  to  measure,  respectively.     It  is  from  these  data 


§  73-   The  Location  of  Ascending  Passage-Way.     133 

that,  it  is  thought,  the  location  of  the  point  C  can  be  re- 
covered. 

Colonel  Vyse  gives  it,  B  D  —  B  0=  3850  —  758  =  3092 

inches  ^  O  D. 
Thislastresult  suggests,  at  once,  a  Parker  (and  pyramid) 
measure — viz.. 

Standard  circumference,   2d6i.2  inches. 
Increased  by  its  one-half,  1030.6 


a 


Together,  3091.8 

By  Colonel  Vyse,  3092.0 

Difference,  .2 


(< 


or  —    of  one  inch,  in  this  many  thousands  of  inches. 
10  •' 

Let  it  be  taken  that  this  measure  of  2061.2  -|-  1030.6  = 

3091.8  was  intended,  as  in  inches,  for  the  distance  from  O 

to  D.    Professor  Smyth  gives  the  value  O  C  at  60.2  inches, 

or  5.01    feet,  and  the   distance  C  C   measuring  from  the 

basement  beginning,  at  1022.2  —  963.0  =  59.2  inches,  or 

4.933  feet ;  or  O  C  +  C'C  =  60.2  +  59.2  =  119. 4  inches  ; 

or  5.01  +  4.933  =  9-943  feet.     Then  for  the  distance  C  D, 

3091.8  —  119.4  =  2972.4    inches, 

or,  247.70  feet. 

By  calculation.  Colonel  Vyse's  measures  of  this  distance 

would  have  been,  247.71  feet. 

Let  the  distance  C  D,  then,  be  taken  at,  2972.4    inches, 

or  247.7    feet. 

Floor  line  of  ascending  -passage-way,  -with  relation  to  the 
base  of  the  pyramid,  to  the  levels  of  the  queen's  and  king's 
chamber,  and  to  the  vertical  axial  line  of  the  mass, 
{b.)     From  data  obtained 

A  C  =  247.70  feet. 
Angle  B  A  C  =  26°  28'  24^1 

"      ACB  =  63°3i'35"9 
"      B=-         90° 


134        Construction  of  the  Great  Pyramid.      §  73. 


Then  A  B  will  equal 
"      BC    " 

C  H  (§  72,  e,  3,)  37.9908  inches 

Then  CB  +  CH  =  BH  = 


221.726871    feet, 
no. 419458    " 
3.16590      " 


113-58535      " 

Note. — To  get  B  C  and  AB,  there  are  proportions  to  be  found 
in  §  64  :  for  there  A  C  -|-  D  B  =  153.2476,  and  A  B  =  343  7745. 
Now,  AC  being  given  at  247.70,  and  being  part  of  the  same 
lines,  we  have  the  proportion, 

343-7745+  :   153-2476+     =:     247.70  :   110.419458  feet, 
and,     3437745:    307.7273     ::     247.70    :   221. 736S71  feet. 

But,  from  H  to  K',  the  base  of  the  pyramid,  is  100  feet, 
as  has  been  taken  ;  then,  B  H  —  H  K'  will  equal  B  K', 
or  the  vertical  elevation  of  the  point  A,  or  intersection  of 
the  floor  line  of  the  ascending  with  the  roof  line  of  the  de- 
scending passage-way  above  the  base. 

This  distance,  or  B  K'  =  113.5853  —  100  =  13-5853+ 
feet. 

(c.)  For  the  measures  of  the  lines  in  the  diagram,  con- 
nected with  the  ascending  passage-way,  reliance  is  had  on 
the  measures  and  results  of  Professor  Smyth.  His  care 
and  painstaking,  one  may  say,  even  increased,  as  to  the 
accuracy  of  his  measures,  as  he  ascended.     Very  great  re- 


§  73-   The  Location  of  Ascending  Passage-Way.     135 

liance  is  evidently  to  be  placed  in  his  results,  even  to  hun- 
dredths of  inches.     He  gives,  as  elements  to  work  by — 
(i.)     The  distance  A  M  of  the  floor  of  ascend- 
ing passage,  123.683  feet 
The  angle  N  A  M  =  26°  6' 
(2.)     The  distance  ML  of  length  of  grand 
gallery  floor  line,  to  where  it  strikes  the 
south  wall  of  same,  156.9  feet. 
The  angle  L  M  R,                                                     26°  17'  37'' 
From  these  angles,  A  M  N  =                                 63°  54' 
and  M  L  R  r=                                                             63°  42'  23" ; 
and,  with  these  angles,  the  following  are  the  values  of  the 
lines  : 

(3.)     AN  =  III. 07 1  feet 

NM=    54.413    " 
(4.)     MR=  140.666   " 
LR=    69.502    " 
{(i.)     AN  +  MR  =  111.071  +  140.666 
=  AF=  251.737      feet 

C  H,  taken  at  37-99o8  [§  72  {e-)  (3)  ],  G  H 

will  be  29.8379  inches,  or,  in  feet,  2.48649    " 

The  distance  from  G  to  the  vertical  axial 

line  of  the  pyramid  was  32.42377    " 

Deduct  GH,  2.48649    " 

equals  from,  say,  H  or  B  to  the  axial  line,       29.93728    " 
or  A  B  +  this  distance  =  221.726871  4- 

29.93728=  251.66415    " 

A  F  has  been  shown  to  be  251.737        " 

Difl^erence,  ,073        '* 

7 
or  —   of  a  foot,  to  which  distance  A  F  is  made  to  project 

be3^ond  the  vertical  axial  line  of  the  structure ;  or  this  ap- 
proximation would  go  to  show  that  the  south  wall  of  the 
grand  gallery  and  the  vertical  axial  line  Avere  in  common, 
because  so  slight  a  variation  was  hardly  to  be  intended. 
At  any  rate,  this  is  considered  to  have  been  the  case,  from 
the  showing. 


136        Construction  of  the  Great  Pyramid.      §  73. 

(e.)  Take  the  vertical  distance  of  L,  on  the  south  wall 
of  the  grand  gallery,  above  the  base  of  the  pyramid — 

(i.)     LR=  69.502    feet 

NM=  54.413      " 

B  K'  to  base  of  pyramid  =^  13-5853    " 
or  a  total  of  137-5003    " 

as  the  height  at  which  the  floor  line  of  the  grand  gallery 
strikes  the  south  wall  of  the  same,  above  (vertically)  the 
base  of  the  pyramid. 

Take  4  times  the  length  of  the  king's 
chamber,  or  34-3774+  X  4,  and  it  is 
equal  to  137.50980  feet 

Compare  these  results — 

L  K  on  the  diagram,  137.5003      " 

4  times  the  king's  chamber  length,  137.5098      " 

Difference,  -0095      " 

or  9  I  1000  of  a  foot. 

li  ynay  be  taken,  then,  that  the  intention  of  this  height, 
as  to  what  it  should  be,  zvas,  that  it  should  be  four  times 
the  length  of  the  king's  chamber,  as  enlarged  on  the  stand- 
ard, or  four-tenths  the  length  of  the  descending  passage- 
way. 

This  value  has  already  been  referred  to  ;  for  137.5097-f- 
feet,  are  1650. 1176  inches,  and  this  value  is  a  diameter  to  a 
circumference  of  5184,  or  the  characteristic  value  of  the  solar 
day,  which  is  5184-000"'.  Here  we  can  see  a  linking 
together  of  values ;  for  the  dimensions  of  the  descending 
passage-way,  are  of  a  nature  that  seems  to  bear  relation 
to  the  square  of  the  earth's  equatorial  diameter ;  and  they 
are  so  framed,  and  located,  as  to  give  this  vertical  height, 
of  a  diameter  of  a  solar  day  value.  A  result  of  this  kind, 
fitting  so  accurately  to  the  uses  of  the  Parker  forms,  fully 
compensates  for  the  detailed  trouble  of  arriving  at  it. 


§  74*      Interior  Geometrical  Construction.         137 


SECTION  X. 

ABSTRACT    GEOMETRICAL    ELEMENTS. 

§  74.  As  all  of  the  elements  of  measure  indicated  are 
seen  to  spring  from  the  use  of  one  geometrical  problem,  it 
is  necessary  to  group  the  results  springing  from  that  prob- 
lem, as  applicable  to  these  various  locations,  together. 

{a.)  The  discovery  of  an  enlargement  on  the  standard 
measure,  that  is,  standard  20612,  enlargement  20626.- 
470017  (§  43,  §  51,  §  54),  growing  out  of  a  principle — viz., 
to  obtain  from  20612,  circumference,  to  6561,  diameter,  the 
formula — 

(i.)  20612  :  6561  :  :  I  :  3183097224917, 
by  which  there  is  obtained  a  circumference  of  tintty,  to  a 
diameter  of  318+,  becomes  of  greatest  consequence  in  the 
construction  of  the  pyramid.  The  application  of  this  en- 
largement on  the  standard  has  served,  as  shown,  to  develop 
the  measures  of  the  king's  chamber,  with  other  features ; 
and  now,  in  connection  with  a  geometrical  exhibition,  it 
will  serve  to  bring  out  the  various  relations  indicated  at  the 
heads  of  this  section. 

{b.)  The  standard  base  of  the  pyramid  is  763.4074074+ 
feet.  31.8309722491  +  ,  the  numerically  new  diameter 
value  to  a  circumference  of  unity,  if  multiplied  by  24,  = 
763.943333980-I-  feet,  as  the  enlargement  on  the  standard 
for  that  base  side.  Take  the  standard  measures  of  the 
pyramid,  viz.,  height  486  feet  to  base  side  763.4074,  and 
find,  with  these,  an  extreme,  of  which  486  is  a  mean  -pro- 
■portional,  as  follows  : 

(i.)  763.4074+  :  486  ::  486  :  309.3970502, 
and  represent  this  geometrically,  where,  as  per  diagram, 
A  D=:  763.4074+,  06  =  309.3970502,  and  CD  =1486. 
It  is  seen  that  the  diameter  of  the  circle  to  represent  this 
mean  proportional  is  763.4074  +  309.397  =  1072.80445+  ; 
and  the  radius  is  1072.80445  -f-  2  =  536.40222+  :  and  these 
measures  are  in  reality  a  commingling  of  standard  and  en- 


138        Construction  of  the  Great  Pyramid.       §  75. 


largement ;  for  the  proportion  is  of  the  same  nature  with  (i.) 

in  (a). 

c 


Length  of  King's   Chamber  Level. 

§  75.  Let  A  be  the  edge  of  the  great  step,  in  the  upper 
and  south  end  of  the  grand  gallery  ;  A  B,  the  passage-way 
level  to  the  king's  chamber,  and  BC,  the  width  of  the  king's 
chamber. 


I — 


3 

— +— 


c 


It  has  been  shown  that  the  width  of  the  king's  chamber 
is  an  enlargement  on  the  standard  of  17.17666+  feet,  or 
ten  cubits,  and  is  206.2647+  inches,  as  enlarged  on  206.12. 
Professor  Smyth  gives  the  measure  A  B  as  330.3^  inches. 
Add  the  two  lengths  :  206.2647  +  330.3  =  536.5647  inches. 
Compare  this  with  the  radius  value  above  : 

Radius  value,  536.40222  inches. 

This  level  length,  536.5647         •' 

Difference,  -1625  " 

Consider  the  king's  chamber  width  as  used  for  this  pur- 
pose at  the  standard y  and  then  add  the  lengths  206.12  + 
330.3=  536-42    inches. 

Radius  above,  536.402      " 


(< 


Difference,  .018 

These  correspondences  are  thought  to  show  the  origin 
of  this  line. 


§  76.       Interior  Geometrical  Construction.         139 

JVote,  that  if  this  .018  of  an  inch  is  taken  as  the  correction  of 
330.3,  as  330. 2S3  inches,  then  we  had  the  equatorial  diameter  of 
the  earth  as  7926. 926S  ~  24  =  330.2886,  thus  showing  a  wonder- 
ful exactitude  of  relation.  3302886  —  330.282  =  .0066  of  one 
inch  difference.  This  is  a  very  strong  corroboration  of  the  truth- 
fulness of  all  the  measures  taken  as  cJiccked  hy  tJiis  result.  As 
seen,  this  result  is  the  half  the  equatorial  diafneter  of  the  earth, 
as  radius.,  divided  into  12  parts ;  showing  a  measure  of  time  and 
earth  distance  relations.  How  exquisite  and  exact  this  is,  in  con- 
nection with  the  Hindu  system,  displayed  in  the  king's  chamber, 
for  working  out  sines,  cosines.,  tangents.,  co-taitgents.,  and  ■plan- 
etary orbits  ! 

Elements  of  Dimensions  of  ^iccn^s  Chamber. 

§  76.  This  geometrical  form  gives  also  the  grand  out- 
lines of  the  queen's  chamber.  The  form  contains,  as  seen 
(§  74),  the  standard  elements  of  measure  of  the  outside  shape, 
and  this  outside  was  clothed  in  -white  as  a  color.  Now,  the 
queen's  chamber  is  in  tuhite,  in  contrast  with  the  king's 
chamber,  which  is  in  red.  The  white  of  the  queen's 
chamber  may,  then,  indicate  a  relation  coming  from  the 
same  source  or  elements  with  the  measures  of  the  exterior. 
Take  it  that  this  is  so,  and  that  the  angle  of  the  roof  of 
that  chamber  is  but  a  copy  of  the  geometrical  form  and  an- 
gle C  B  E,  §  74.  The  angle  C  B  E  =  57°  31'  o6".3  X  2  =- 
115°  02'  I2"6,  and  this  is  taken  to  represent  the  angle  of 
the  roof  of  the  queen's  chamber.  The  line  C  E  corre- 
sponds with  the  north  and  south  length  of  the  room,  and 
Professor  Smyth  gives  this  length — 

On  the  east  side.,  at  206.5  to  204.7. 

On  thQ  west  side,  at  206.0  to  206.3. 
These  but  serve   to  indicate    the  real  measure  of  206.12 
inches,  as  a  radical  standard  measure.     There  is  given, 
then,  the  length  C  D  =  103.06,  and  the  angles  C,  D,  and 
B,  to  find  the  lines  D  B  and  C  B  ;  and  these  are — 

(i.)     DB=    65.5766  inches. 
CB  =  122.108        " 
As  this  is  but  a  reduced  form  of  the  geometrical  problem, 
then — 


140         Construction  of  the  Great  Pyramid.       §  76. 

(2.)  309-397  :  65.5766  ::  763.4074  :  161.803, 
and  the  circle  of  the  queen's  chamber,  thus  indicated,  would 
have  a  diameter  of  161.803  +  65.5766  =  227.379+  inches  ; 
and,  in  fact,  this  does  indicate  the  measured  length,  east 
and  west,  of  this  very  chamber,  for  Professor  Smyth  gives 
this  measure  at — 

On  the  south  wall,  227.4 

On  the  north  wall,  226  to  226.5 
Compare  this  measure,  227.379 

with  Professor  Smyth's,  227.4 

Difference  ( of  an  inch  | ,         .021 

\  100  ) 

Thus  the  proportionate  and  basic  measures  of  the  queen's 
chamber,  as  to  all  but  the  heights  from  the  floor,  which  is 
in  the  rough  and  unjinishcd  (which  seems  to  show  that  the 
elements  of  measure  as  relates  to  the  floor  were  not  to  be 
taken  into  consideration),  become  restored  in  terms  of  this 
geometrical  problem,  and  in  the  use  of  the  standard  meas- 
ures (as  in  contrast  with  those  of  the  king's  chamber,  which 
are  in  measures  enlarged  on  the  standard),  as  follows: 
(3.)  Lengthof  the  room  north  and  south,  206.12      in. 

*'         "        "     E.  &  W.  (one  meas.),    227.379     " 
"     of  incline  of  roof,  122.108     " 

Height  of  room  in  the  gable,  65.5766  " 

Not  only  so,  but  these  measures  are  all  connected  to- 
gether under  one  problem,  inasmuch  as  the  height  line  re- 
jected as  indicated  by  the  unfinished  floor,  is,  yet,  set  forth 
in  another  element — viz.,  the  length  east  and  west — as 
227.379,  as  the  diameter  of  the  circle,  of  which  the  extremes 
are  161.803  and  65.5766,  to  copy  the  form  in  §  74.  Sub- 
ject to  the  different  measures  raised  by  reason  of  the  biased 
line,  the  beautiful  harmony  and  outcome  of  these  measm-es 
from  these  proportions,  seems  to  stamp  them  as  correctly 
taken,  agreeably  with  the  basic  or  standard  idea  of  the 
architect. 

It  is  but  right  to  say  that  there  is  a  serious  discrepancy 
between  the  measures  of  Colonel  Vyse  and  Professor 
Smyth  as  to  the  measured  height  of  the  walls,  and  of  the 
gable,    or   D  B  distance.      Colonel  Vyse  gives  the  total 


§  76.      Interior  Geometrical  Construction.         141 

height  at  243  inches  from  the  floor  (or  from  some  recognized 
mark  or  line  above  the  rough  and  unfinished  bottom). 

He  gives  the  distance  D  B  as  66.  inches, 
closely  approximating 65.5766,  considering  the  difficulty  of 
obtaining  this  measure.  How  he  took  his  measures  is  not 
known  ;  but  it  is  strange  that  in  the  number  243  he  has  hit 
upon  the  exact  numerical  value  of  the  half  height  of  the 
great  pyramid  taken  at  the  standard,  and  243  —  65.5766  = 
177.4234,  which  is  extremely  close  to  355  X  .5  =^  177-55  to 
a  diameter  value  of  113  X  -5  =56.5,  which  is  the  founda- 
tion measure  of  Moses  in  the  construction  of  the  Taber- 
nacle. Had  these  proportions  been  intended,  the  gable 
would  have  been  65.6,  and  the  diameter  would  have  been 

.06 
227.46;  differing  from  Professor  Smyth's  by    of  an 

inch — an  allowance  very  readily  to  be  made  in  the  difficult 
conditions  of  the  room. 

(a.)  (It  is  well  to  note  here,  that  in  this  queen's  chamber  seems 
to  be  the  use  of  the  1 13  to  355,  or  Hebrew  form,  with  relation  to, 
or  in  connection  with,  the  Parker  or  pyramid  relations  6561  to 
5153  X  4=  20613.  One  such  relation  has  just  been  shown. 
Great  stress  is  laid  in  the  Bible  upon  the  word  for  hcel^  occurring 
as  it  does  in  the  Garden  of  Eden,  and  being  the  name  of  yacob^ 
who  was  the  father  of  the  division  of  the  year  into  12  and  13 
months.  Reading  the  values  of  the  letters  of  this  word  which 
is   iDpT^,  and    there  is  712    (which    may  also  be  used  as  217). 

Mark  the  uses,  or  one  use —  

712  :     226.63,  or  113.31    X  2. 

356  :      113  31 

6561  :     226.62 

113-355  '  356-115 
It  thus  appears  that  713  is  a  circumference  to  226.62  as  a  di- 
ameter. It  was  shown  that  1 13.+  was  a  circumference  to  36,  and 
that  two  were  used  in  the  Garden  of  Eden,  or  113  X  2  =  226. 
(See  §62  («.),  §86,  §87.)  Now,  it  is  most  strange  that  in  the 
Hindu  personified  representation  of  this  garden,  a  female  is  repre- 
sented as  bending  the  heel  of  the  left  foot  before  and  touching  the 
mouth  of  the  pudenda,  which  of  itself  is  characterized  by  the 
number  7,  as  the  female  time  originating  number,  and  circle  of 


355 

113 

20612 

356 

20613 

712 

6561 

20612 

142        Construction  of  the  Great  Pyramid.      §  76. 

the  week;  so,  thus  713,  or  the  heel,  in  this  use,  thus  becomes 
marked  as  the  pudenda,  or  a  circle  of  time  [§92,  (a.)  (<5.)  (d.)  ]. 
In  fact,  Hargrave  Jennings,  in  Rosicrucians,  page  332,  says: 
"  The  late  Dr.  Donaldson  has  a  dissertation  upon  the  word  ^p  V? 
Jacobs  which  is  translated  '  heel^  in  Genesis  iii.  15.  He  adduces 
Jeremiah  xiii.  22,  and  Nahum  iii.  5?  and  comparing  the  words 
made  use  of  in  the  original,  shows  that  the  '•heel'  is  a  euphem- 
ism, as  are  the  ''feet '  in  Isaiah  vii.  20.  His  exhaustive  argument 
demonstrates  that  the  part  intended  to  be  signified  by  the  word 
is  pudenda  muliebria."  One  value  of  the  words  Garden  of 
Eden^  as  added,  is  177,  and  this  is  the  height  with  the  gable  of 
dd,  which  Colonel  Vyse  takes  to  make  up  his  243.     When  Jacob 

had  his  name  changed,  it  was  to  Js  (or  Jcs),  R  A  L,  J^CVU'*', 
or  13-213;  where,  from  "  y  (or  yah),  is  heel"  or  712,  it  now 
becomes  "  yes  (or  ycsus),  is  213,"  which  is  also  the  Hebrew 
word  head,  or  t^X")'  ^^  "  y^^  (Ji^^  ^  form  of  '  man '),  is  hcadf 
and  head,  or  213,  is  355  X  6  =  213.0,  the  form  of  the  first  word 
in  Genesis.) 

There  is  some  confusion  in  the  methods   employed  by 
Professor  Smyth.     He  takes  the  height  of  the  walls  at 

"  182?     184.5?   Mean,  183.2 
181?     182?  "        181.5 


Mean,  182.4" 

apparently  bringing  out  the  value  182.5  x  2  ^  365.  It  is 
possible  that  this  was  intended  as  permissible,  in  a  variable 
height,  or  as  leaving  an  open  value.  Independently  of  this 
he  takes  the  gable  measures  at 

245.4     244.9  niean,  245.2 

244.2     000.         "        244.2 

243.9     000.  '*       243.9 


Mean,  244.4 

■which  show  that  there  may  have  been  some  indication  or 
mark  noticed  by  Colonel  Vyse,  fastening  him  to  the  meas- 
ure 243.  Professor  Smyth  then  works  out  244  —  182.4  =  62. 
inches,  for  the  gable  height,  in  place  of  66.  by  Colonel 
Vyse. 

There  is  but  this  to  be  said,  that  where  the  floor  is  in  the 


§  77*       Interior  Geometrical  Construction.         143 

rubble,  and  evidently  uneven,  it  would  seem  that  a  set  of 
measures  on  the  sides,  averaged,  would  not  be  at  all  a  cer- 
tain measure  to  be  deducted  from  the  gable  measures,  taken 
in  the  center  of  the  room,  because  one  is  not  sure  of  a  com- 
mon -plane  of  measure.  Any  departure  from  accurate 
measuring,  however,  or  from  a  sound  judgment  as  to  proba- 
ble relations  of  parts,  would  be  a  wonder  in  the  practical 
labors  of  Professor  Smyth. 

Passage  to  ^ieen''s  Chamber. 

§  77.  Bearing  in  mind  that  the  level  of  the  floor,  from 
the  edge  of  the  great  step  to  the  king's  chamber,  comes 
from  the  geometrical  formula  (§  74)  {b.),  (2.),  (see  also  §  75), 
and  that,  by  a  proportional  use  of  the  same,  the  proportions 
of  the  queen's  chamber  are  produced,  the  following,  giving 
the  length  of  the  passage-way  to  the  queen's  chamber, 
from  the  use  of  the  values  in  the  same  problem,  seems  to 
have  weight. 

{a.)     The  number  309.397050  is  but  an  enlargement  on 

the  value,  as  to  its  kind,  of  20612,  as  follows  ;  Add  to  the 

latter  the    half   of   itself,   and    there  results,   in    standard 

measure— 

(i.)  20612  -f-  10306  =  30918. 

The  enlargement  on  the  king's  chamber,  taken  at  the  stand- 
ard measure  of  34-3533-f-?  was — 

(2-)     34-3577450'  and  this  X  9  =  309.397050, 
as  above.     Then,  309.397050  is  but  an  enlargement  on  the 
standard    measure    309.18.       The    difference    is    .217050. 
Raise  this  difference,  thus — 

(3.)      217.050  X  7  =  I5I9-35C*. 
If  this  be  taken  as  1519.350  inches,  it    agrees  with    the 
length  of  the  passage-way  from  the  north  wall  of  the  grand 
gallery  foot  to  the  entrance  of  the  queen's  chamber,  as  fol- 
lows— 
(4.)     Professor  Smyth's  measure  of  same,  1519.400  inches. 

From  (3)  above,  1519.350      " 

Difference,  of  an  inch.  .05 


144        Construction  of  the  Great  Pyramid.       §  78. 

Hence,  it  would  seem  that  this  passage-way  is  seven  times 
the  difference  between  the  standard  30918,  and  the  enlarge- 
ment on  the  same  of  30939705-I-,  or  the  extreme  of  the 
g,eometrical  problem. 

There  is  a  slight  confirmation  of  the  fact  of  1519.350 
being  used  as  a  multiple  of  seven  times  this  difference,  in 
the  closing  description  of  the  length  of  this  passage,  as  to 
its  being  marked  off  in  certain  divisions.  Professor  Smyth 
says  :  "  The  above  measures  for  length  being  the  mean  of 
two  sets,  nowhere  differing  more  than  0.3  inch,  and  hav- 
ing been  further  tested  for  the  whole  length,  by  a  third 
measuring  carried  on  by  rod  lengths  of  100  inches,  may  be 
pretty  safely  depended  on.  Hence,  whole  length  of  hori- 
zontal passage  from  north  wall  of  grand  gallery  to  north 
wall  of  queen's  chamber  (inches),  15 19.4 

"  One-seventh  of  the  above,  217. i 

*'  South  length  of  passage  with  low  level,  216. i 

"  North  length,  without  roof,  measuring  to  mean 
■place  of  the  two  cuts-off  in  grand  gallery 
floor,  217.8." 

It  may,  then,  be  taken  that  the  source  whence  this  length 
of  1519.35  is  obtained  is  as  stated;  and  that,  very  likely, 
it  has  something  to  do  with  seven  of  the  spaces  or  stripes 
of  the  grand  gallery. 

Heights  from   Floor  of  Subterranean  Passage -Way  to 
the  Gable  Roof  of  CampbelPs  Chamber. 

§  78.  {a.)  A  still  further  application  of  this  same  geo- 
metrical problem,  it  is  thought,  can  be  made  as  to  the 
heights  of  the  various  chambers  terminating  in  Campbell's 
chamber,  above  the  floor  level  of  the  king's  chamber ;  that 
is,  from  the  gable  of  Campbell's  chamber  to  the  king's 
chamber  level.  Upon  a  careful  examination  of  the  angle 
of  the  roof  inclines  of  Campbell's  chamber,  on  Perring's 
plates  of  Vyse's  measures,  it  measures  ii5°d=,  and  appears 
to  be  the  same  angle  with  that  of  the  queen's  chamber  roof. 
That  they  are  intended  to  represent  this  same  angle,  is,  in 
a  measure,  confirmed  by  the  fact  that,  while  the  rest  of  the 


§  78.      Interior  Geometrical  Construction.         145 

chambers,  up  to  this  one,  are  in  red  granhe,  return  is  made, 
in  the  roof  of  this  chamber,  to  the  -white  of  the  exterior, 
and  of  the  queen's  chamber.  Referring  to  the  geometrical 
problem  (§  74),  it  is  seen  that  the  angle  spoken  of  is  made 
by  use  of  the  number  309397050,  which  has  been  shown 
to  be  an  enlargement  on  the  standard  of  309.18,  which  last 
is  the  measure  giving  rise  to  the  point  of  intersection  of 
the  descending  with  the  ascending  passage-way. 

Take,  now,  the  standard  and  enlarged  lengths  of  the 
king's  chamber,  and  multiply  them  by  9 — 

(I-)     34-35333+  X  9  =  309-18  feet, 
(2.)     34.3774X9  =  309-397050^^^1, 
giving  these  identical  values. 

(<5.)     By  the  Parker  time  problem — 

(i.)     20.612  X  —  =  27.4826664-, 
o 

which,  agreeably  to  Mr.  Parker,  "  is  the  exact  value  of  the 

passage  of  the  moon  round  the  earth  over  the  value  of  a 

complete  circle,  the  time  being  in  circular  days  of  23h. 

51'  23"  20'"  each  (5153-000'")  ;  and  therefore  27.482666+ 

X  5153000'"  (the  value  of  one  circular  day)  =  141618181.- 

333"^ — '~  5184000'"    (the  value   of  one   solar   day)  =  27.- 

3183220164,  which,  reduced  to  the  proper  divisions  of  solar 

time,  equals  27d.  7h.  28'  23"  i'"  20"",  which,  I  say,  is  the 

exact  time  of  the  passage  of  the  moon  around  the  earth." 

To  this  is  to  be  added  4'  40"  46'",  or  the  difference  between 

one  circular  and  one  sidereal  day,  as  shown  in  §  13. 

{c.)     Divide  the  Parker  formula  by  12,  where  20.612  is 

taken  to  be  in  inches,  and  there  results — 

4        27.48266 
(I.)     i.7i7666x|-=    -^^7^—, 

where  the  first  term  has  become  the  value  of  one  cubit  in 
British  feet,  and  the  last  term  has  become  the  circular  value 

of  —  of  one  lunar  month.  Multiply  by  10,  and  there  re- 
sults— 

4       274.8266 
(2.)     17.1766+  X^=     '^^^       , 


146        Construction  of  the  Great  Pyramid.      §  78. 


where  the  first  term,  or  standard  width  of  king's  chamber, 

10 

has  become  10  cubits,  and  the  last  has  become  — of  one 

12 

lunation. 

Clear  of  fractions,  and  there  results — 

12       4 
(3.)     206. —  X  -=  274.8266+, 
o 

where  the  first  term  has  become  120  cubits  in  British  feet, 
and  the  last  has  become  10  lunations.  (As  to  the  great  es- 
timation of  the  Parker  form  20612,  raised  to  the  value  of 

12 
120  cubits,  or  206.  —  British  feet,  see  Appendix,  iii.) 

But  while  this  result  is  so,  agreeably  to  Parker,  the 
standard  length  of  the  king's  chamber  multiplied  by  8 
gives  this  very  value^  or — 

(4-)     34-35333+  X  8  =  274.8266+  feet. 

{d.)  The  standard  circumference  of  the 
pyramid  is  36643.55+  inches  to  a  height  of 
486  feet.  But  366.4355+  is  that  value  which 
Mr.  Parker  says  is  "the  exact  time  of  the 
earth's  motion  round  the  sun,  over  the  value 
of  a  complete  circle  in  space,  the  time  being 
in  circular  days,"  on  which  he  proceeds  to 
give  the  exact  value  of  the  year  in  solar 
time.  One-fourth  of  this  36643.55,  reduced 
to  feet,  is  763.4074+ ,  the  base  side  of  the 
pyramid  ;  and,  by  the  geometrical  problem — 
(i.)  763.4074+  :  486  ::  486  :  309.397050, 
whereby  it  is  seen  that  this  309.397+  is  a  re- 
duction of  the  measure  of  solar  time,  while 
274.826+,  or  8  times  the  length  of  the  king's 
chamber,  is  a  measure  of  lunar  time.  It  is 
also  seen  that  while  763.  to  486  is  in  the  form 
of  I  :  314159,  486  to  309.397  is  in  the  form 
of  .318309  :    I. 

{e.)     Take,  then,  the  following  measures 
for  comparison  ; 


i 


§  78.       Interior  Geometrical  Construction.         147 


(i-)     34-3533  X  9  =  309-18    standard. 

34.3774  X  9  =  309-397  enlargement. 
34-3533  X  8  =  274.826  standard. 
(2.)     Let  A  B  =  309.18  feet. 

Let  C  B  =  274.826+  feet. 
Then  AB  —  BC  =  34.3533+  feet,    or   the   standard 
length  of  the  king's  chamber. 

With  C  as  a  center,  and  AC,  or  34-3533+'  as  a  radius 
(see  preceding  diagram),  describe  the  inner  circle  A  D ; 
then — 

(3.)     274.826  —  34-3533+  =  240.4733, 
or  34-3533  X  7  =  240.4733- 
Now,  instead  of  the  standard  measure  309.18,  make  use 
of  the  enlarged  measure  309.397050;  then — 

(4.)  309.397050  —  274.8266  =  C  E  =  34-570383+- 
Then,  with  C  as  a  center,  and  C  E  as 
radius,  describe  the  outer  circle  E  E' ; 
then — 

(5.)   EE'=34.570383X  2  =  69.140766 

feet ; 
and  this  is  taken  to  equal  the  height  of 
the  gable  of  Campbell's  chamber  from 
the  level  of  the  floor  of  the  king's  cham- 
ber ;  while  E  B  is  taken  to  be  the  total 
distance  from  that  gable  to  the  floor  of 
the  passage  to  the  subterranean,  by  the 
rejection  of  the  number  value  of  216330, 
on  which  value  the  entire  pyramid 
works  seem  to  be  founded. 

A  B.  Roof  of  Campbell's   chamber 
to  level  of  king's  chamber  floor. 
B  C.  Space  filled  above  C. 
C  D.  Distance  to  base  of  pyramid. 
D  E.  Distance   to  subterranean  pas- 
sage floor. 

E  F.  Distance  of  2.16330. 


jp.. 


E 


148       Construction  of  the  Great  Pyramid.      §  79. 

(6.)     From  A  to  F,  the  dotted  line,  probably  marked  in 

the  subterranean  chamber,  is  309'397050  feet. 

AB,  as  taken  in  (5.),  is  69.140767 

B  C  is  the  filling  of  the  king's 
chamber  level  above  the 
intersection  of  the  floor 
line  of  the  grand  gallery, 
with  the  south  wall  there- 
of. Professor  Smyth 
makes  this  7  inches,  or 
•5833  of  a  foot.  Take 
it  at  .583183 

C  D  =  (§  73,  E)  (to  base  of 

pyramid),  137.509800 

D  E  =  (to  floor  of  subterra- 
nean passage),  100.000000 

E  F  =  as  taken,  2.163300 

309.397050  feet. 
Thus  it  is  seen  that  the  detailed  measures,  as  variously 
found,  as  to  vertical  heights,  amount  in  the  aggregate  to 
the  extreme  of  this  geometrical  problem,  which  is  em- 
braced in  the  angle  of  115°  (§  76),  and  is  marked  on  the 
diagram  as  D  B  (§  74).  All  the  values  have  been  worked 
out  and  accounted  for,  save^  only,  the  183   of  .583183  for 

•5833 »  where  of  a  foot  has  been  borrowed,  or  rather 

taken  from  Professor  Smyth's  measure.     What  is  of  the 
greatest  significance  seems  to  be  the  number  value  of 

216330, 
to  make  up  the  perfect  value  of  309.39705. 

Height  of  Level  of  Passage  to  ^iccn's  Chamber^  above 
the  Center  of  the  Sphere,  in  -which  the  whole  Pyramid 
is  Supposed  to  have  been  Placed. 

§  79.  Rejecting  216330  from  the  radius  of  the  circle 
[§  55  (^0]'  o""  610.63823 216330=610.42190,  that  ra- 
dius becomes  610.42190  feet.     From  this  deduct  586  (the 


§  79-      Interior  Geometrical  Construction.         149 

standard  height  of  the  pyramid,  or  486,  fliis  the  distance 
vertical,  from  base  of  pyramid  to  bottom  of  subterranean 
passage-way,  or  100  feet),  and  there  remains,  from  the 
bottom  of  the  subterranean  passage-way  to  the  center  of 
the  sphere  (216330  rejected),  the  distance  of,  as  shown — 

24.42190  feet. 
Add  the  distance  from  bottom  of  subterra- 
nean passage-way,  less  the  height  of 
the  passage,  or  100  —  3.16590,  =  96.82530    " 

Add  from  the  base  of  pyramid  to  the  level 
of  the  intersection  of  the  ascending 
and  descending  passage-ways  =:  IS-S^SSS     " 

Add  height  from  this  intersection  to  level 

of  queen's  chamber  passage  =  54.41300    " 

Add,  as  borrowed,  one  cubit,  i. 71766    " 


And  there  results  a  total  of  190.96321     " 

or,  a  wonderfully  close  approximation    to  ten   times  the 
height  of  the  king's  chamber,  or  190.98583  feet. 
Compare  the  value  190.96321     " 


The  difference  is,  .02262    " 

or,  numerically,  just  one  of  the  lengths  of  the  queen's  cham- 
ber itself,  or  113  X  2  ^226.  Let  the  formula  be  recalled 
from  §  35  (3),  as  follows : 

(i.)     113   :  355.0001-f     ::     36  :   113.0973  +  , 

where,  as  was  shown,  the  object  was  to  get  't,6,  or  the  factors 

6  X  6,  as  a  straight  line  value,  in  place  of  a  circular  value, 

as  in  the  king's  chamber,  where  19.0985  is  proved  to  be  a 

diameter  to  a   circumference  of  60.     Multiply  this  fourth 

term  by  2. 

(i.)     113.0973+ X  2  =  226.1946, 

and  the  above  difference  is  found  to  be  the  of  one. 

1000 

It  is  quite  interesting  in  this  connection,  as  to  the  dimen- 
sions of  the  queen's  chamber,  that  while  its — basic  length 

north  and  south  has  been  shown  to  be  5153  X  2  ^  103.06 
inches,  or  twice  the  value  of  the  area  of  the  circle  inscribed 


150        Construction  of  the  Great  Pyramid.      §  79. 

in  the  square,  under  the  Parker  forms,  in  its  basic  length 

cast  and  west  it  is  thus  seen  to  be  113  X  2  =  226  inches, 

or  twice  the  Metius  diameter. 

(fl.)     The  rejection   of  216330,  and  the  use  of  a  cubit 

value  of  1.71766+  to  produce  these  singular  results,  calls 

to  mind  a  phase  of  the  self-same   nature   in  this   strange 

work.  Refer  to  the  diagram,  §  55  («.).  Take  the  full  radius 

line  of  the  sphere  ; 

It  is  610.638234  feet. 

Reject  from  this  .216330    " 


And  there  remains  610.421904 

Enlarge  this  by  one  cubit,  1.7 17666 


<( 


And  let  this  be  a  new  radius  of  612.139570    " 

Then  making  use  of  the  formulation  in  §  56  (5.)  : 

Si7i.  81°  51'  i4."5        9-995595 

Sin.  38°o8'45."5        9-790754 

Log.  612.139570         2.786850 

Log.  381.9517+  2.582009 

as  the  value  of  the  line  of  30°  to  F,  to  that  extent  O  D",  at 

which  it  intersects  the  slope  line  of  the  pyramid.    The  sine 

of  this  as  an  angle  of  30°,  is  -,  or  190.975+  feet,  or  .010 

of  a  foot  less  than  ten  times  the  king's  chamber  height. 
Take  the  values  found  above,  and  add  them. 

(i.)     190.985 

190-963 
3810948 
The  mean  of  these  values  is  190.975  feet, 
or  this  very  result,  thus  arrived  at  by  another  way,  but  at 
the  same  time  by  use  of  the  same  rejections. 

(3.)     This  number  216330  becomes  again  manifested  in 
very  important  measures — viz.,  those  of  the  king's  chamber 
level,  and  those  of  the  base  of  grand  gallery — thus  : 
(i.)     From  edge  of  great  step  to  south 

wall  of  the  king's  chamber  (§  75),         536.402  inches. 
(2.)     MR  on  the  diagram  [§73  (<^.)], 
or  base  of  the  grand  gallery  triangle , 
to  south  wall  of  same,  1687.992 

Or  a  total  of  2224.394 


(( 


§8o. 


Interior  Geometrical  Construction. 


151 


61.00  inches. 


But  there  has  been  in  these  additions  a 
lap  of  the  length  of  the  great  step, 
which  by  Professor  Smyth  is  meas- 
ured at  60.8  to  61  inches.  Deduct 
the  larger  measure, 
And  the  result  in  inches  and  decimals  of 

an  inch  is  2163.394       " 

or  che  appearance  in  this  quarter  of  this  remarkable  num- 
ber. 

A  Method   of  -placing  a    Salient  Height  Line  for  the 
Interior  Construction  of  the  Pyranzid. 

§  80.  Take  a  line  equal  to  the  standard  length  of  the 
base  side  of  the  pyramid.  On  this  line  raise  a  square, 
which  divide  into  four  equal  squares.  And,  on  the  base 
line,  construct  the  exterior  lines  of  the  pyramid. 

A  B  =  763.4074  feet.    Then  F'D  will  equal  381.7037  feet, 
as  will  also  A  F'.     On  A  Braise 
the    pyramid    in    the    standard 
measures.        Then    C  F'  =  486 

feet.     At  D  with — ^the  standard 

2 


/n 

e 

// 

\\ 

U— 

\> 

/         ^ 

\ 

486 

height,  or  —  =  243  feet,  meas- 

ure  down  to  F ;  then  with  the 
value  243  for  height,  draw  in 
the  pyramid  D  E  E',  and  it  will 
be,  as  to  its  dimensions,  reduced 

by  just  one-half  from  the  original — that  is,  its  half  base 
side,  now,  will  be  190.8513  +  ,  on  which  the  enlargement 
190.985+  has  been  shown  to  play  so  great  a  part  in  the  pyr- 
amid measures.  By  this  process,  it  will  be  seen  that  the 
works  on  the  E  E'  level,  with  these  proportions,  would  be 
precisely  as  if  they  were  located  on  the  base  of  the  larger 
pyramid  ;  while,  at  the  same  time,  an  elevation  has  been 
obtained  to  work  out  other  results. 

(i.)     In  §  73  {e.),  the  vertical  distance  from  the  base  of 
the  pyramid  to  the  level  of  the  true  floor  of  the  king's  cham- 


152        Construction  of  the  Great  Pyramid.      §  81. 

ber  was  shown  to  be  four  times  the  length  of  the  king's 
chamber  taken  as  enlarged, 

or  34-3774  X  4=  137-5096  feet.  . 

D  F' is  equal  to  381.7037  —  243  138.7037     " 
Difference  in  excess,  1.1941     " 

In  §  73  [a.),  to  obtain  the  distance  247.70  feet,  from  the 
foot  of  the  roof  line  of  the  descending  passage-way  to  the 
point  of  intersection  of  the  floor  line  of  the  ascending 
passage-way,  we  had  the  primary  distance  3091.8,  and  from 
this  there  was  deducted  to  get  the  point  desired,  119. 4 
inches,  or 

3091.8  —  119.4=  2972.4  inches, 
=    247.7  feet. 

The  distance  of  the  remove,  then,  of  this 
point  was  by  a  deduction  from  the 
primary  value  of  ii9'4  inches. 

To  obtain  a  like  remove  to  get  a  particular 
vertical  height,  as  just  shown,  requires 
a  deduction  from  a  primary  value,  of        i-i94  feet. 

All  which  goes  to  show,  that  probably  all  the  interior 
work  of  the  pyramid,  is  to  be  obtained  by  use  of  squares, 
in  their  subdivided  parts. 

§  81.  It  is  thought  best  to  close  the  effort  at  reconstruc- 
tion of  the  great  pyramid  at  this  point.  Many  more  meas- 
ures and  harmonies  could  be  shown — as  of  the  coffer  and  as 
of  the  descending  passage-way  relations  ;  but  it  is  thought 
that  all  has  been  shown  that  is  necessary  for  this  work. 
Now,  let  the  reader  reflect  upon  what  has  been  done  or  ex- 
hibited, (i.)  An  abstract  elemental  relation  of  geometrical 
shapes.  (2.)  A  special  numerical  integral  relation  is  shown, 
as  applying  to  the  notation  and  working  together  of  these 
shapes.  (3.)  With  this  relation,  as  connected,  it  is  thought, 
with  very  beautiful  geometrical  displays,  the  pyramid 
structure,  as  to  its  outside  and  as  to  its  inside  works  and 
measures  and  proportions,  has  been  reproduced  in  measure 
after  measure,  little  and  great,  in  angle  after  angle,  and  in 
general  relations  of  parts  to  parts  ;  all,  so  that,  one  may  say, 
the  results  answer  absolutely  to  the  Briiish  measures  as 


§  8i.      Interior  Geometrical  Construction.         153 

taken.  Surely,  then,  the  diagrams  and  intentions  of  the 
architect  have  been  displayed  and  set  forth,  as  to  the  prac- 
tical architectural  work.  But,  wliat  is  more,  is  that  it  is 
just  as  certain  that  his  mathcfuatical,  and  astronomical, 
and  geographical,  measuring  intents  have  been  disclosed  in 
a  general  sense  ;  and  even  more  than  that.  It  only  re- 
mains to  discover  those  curious  underlying  laws  for  cosmi- 
cal  construction,  certainly  known  to  him,  by  which  the 
cosmos  could  be  so  outlined  that  the  sizes  and  times  of 
planets  could  be  numerically  notated,  and,  by  a  practicable, 
realizable,  unit  of  measure,  co-ordinate  one  with  the  other. 
If  this  statement  is  true,  then  it  must  be  admitted  that  all 
that  has  been  set  forth  has  depended  upon  the  work,  and 
numerical  elements  applied  to  geometrical  shapes,  of  John 
A.  Parker. 

As  to  what  the  extent  of  ancient  knowledge  really  was, 
modern  opinions  are  becoming  more  and  more  liberal  with 
increased  research. 

Mr.  Rawlinson,  in  App.,  Book  XL,  chap,  vii.,  says  :  "  No  one  will 
for  a  moment  imagine  that  the  wisest  of  the  Greeks  went  to  study  in 
Egypt  for  any  other  reason  than  because  it  was  there  that  the 
greatest  discoveries  were  to  be  learnt,  and  that  Pythagoras  or  his 
followers  suggested,  from  no  previous  experience,  the  theory  (we 
now  call  Copernican)  of  the  sun  being  the  center  of  our  system  ;  or 
of  the  obliquity  of  the  ecliptic,  or  the  moon's  borrowed  light,  or  the 
proof  of  the  milky  way  being  a  collection  of  stars,  derived  from  the 
fact  that  the  earth  would  otherwise  intercept  the  light,  if  derived 
from  the  sun,  taught  by  Democritus  and  by  Anaxagoras,  according 
to  Aristotle,  the  former  of  whom  studied  astronomy  for  five  years 
in  Egypt,  and  mentions  himself  as  a  disciple  of  the  priests  of 
Egypt,  and  of  the  Magi,  having  also  been  in  Persia  and  Babylon. 
The  same  may  be  said  of  the  principle  by  which  the  heavenly 
bodies  were  attracted  to  a  center,  and  impelled  in  their  order,  the 
theory  of  eclipses,  and  the  proofs  of  the  earth  being  round. 
These  and  many  other  notions  were  doubtless  borrowed  from 
Egypt,  to  which  the  Greeks  chiefly  resorted,  or  from  the  current 
opinions  of  the  '  Egyptians  and  Babylonians,'  the  astronomers  of 
those  days,  from  whose  early  discoveries  so  much  had  been  de- 
rived concerning  the  heavenly  bodies.  Cicero,  on  the  authority 
of  Theophrastus,  speaks  of  Hycetas  of  Syracuse,  a  Pythagorean, 


154  Pyramid  Symbolization.  §  8i. 

having  the  same  idea  respecting  the  earth  revolving  in  a  circle 
round  its  own  axis  ;  and  Aristotle  observes  that,  though  the 
greater  part  of  philosophers  say  the  earth  is  the  center  of  the 
system,  the  Pythagoreans,  who  live  in  Italy,  maintain  that  fire 
is  the  center,  and  the  earth,  being  one  of  the  planets,  rotates 
about  the  center,  and  makes  day  and  night.  This  heliocentric 
system  (having  been  lost)  was  finally  revived  in  Europe,"  etc. 

The  trouble  was  that  this  kind  of  knowledge  was  of  the 
friestly  caste,  and  therefore  was  utterly  unknown  to  the 
world;  for  this  caste,  with  its  power  of  influence,  would 
discourage  any  theories  tending  to  the  truth,  and  would,  if 
possible,  make  any  one  recant  a  pretended  discovery,  if  it 
chanced  to  militate  against  the  hidden  knowledge. 

Here,  it  has  been  shadowed  forth,  not  only  how  exten- 
sive and  valuable  this  knowledge  was,  but  the  very  nature 
and  groundwork  of  the  knowledge  itself,  yohn  A.  Par- 
ker's tnethod  of  quadrature,  and  his  proble?n  of  three  re- 
volving bodies,  evidently  did  lay  at  the  base  of  the  famous 
Egyptian  and  Pythagorean  systems. 

Thus  the  lines  of  the  admeasurements  of  the  interior 
work  of  the  pyramid,  having  their  origin  from  the  inter- 
section of  the  floor  line  of  the  descending  passage-way 
with  the  sloping  side  line  of  the  exterior,  close  themselves; 
and  that  so  accurately,  tested  in  such  various  ways,  that  it 
seems  it  can  be  safely  said  that  this  work  exhibits  the  res- 
toration or  reconstruction  of  the  pyramid,  agreeably,  in  a 
general  way,  to  the  architectural  plan  and  measures  of  the 
original  designer — what  is  left  to  be  discovered  being  the 
particularities  or  minute  details  of  elaboration  of  his 
thoughts  and  measures. 


SECTION  XL 


PYRAMID    SYMBOLIZATION. 


§  82.     (a.)  In  terminating  this  effort  at  reconstruction  of  the 
pyramid,  it  is  well  to  give  symbolic   representations,  with  their 


§  82.  Pyramid  Symbolization.  155 


meanings,  of  its  elements.  It  is  seen  in  §  55  (a.),  that  the  orig- 
inal pyramid  from  whence  the  real  pyramid  of  the  Nile  springs, 
is  directly  constructed  from  the  original  elements  of  relation  of 
diameter  to  circumference  of  a  circle.  This  is  circular  elements 
one.  On  the  lines  of  this  original  pyramid  springs  another, 
whose  elements  are  circle  fwo.  In  §  74  (^.),  out  of  the  elements 
of  /wo,  another  set  of  elements  is  obtainable,  governing  the  in- 
ferior work  of  the  pyramid  proper ;  these  elements  are  those  of 
circle  three. 

The  elements  of  one  are : 

(i.)     Height,  6561  inches,  546.75         feet. 

—  base  side,  5153  "        429.416-I-    " 

2 

—  base  diagonal,  7287.44-}-      "        607.28-I-      " 

Radius,  7327.65-I-      "         610.63+       " 

The  elements  of  two.,  as  has  been  shown,  are   taken   from  the 

elements  of  one.     Whereas,  the  full  circumference  of  base  of  one 

is  5153  X  8  =  41224  inches,  or  one  hundred  times  the  length  of 

the  king's  chamber,  the  circumference  of  the  pyramid  proper  is 

5153  X  4  (=  20612)  X  ^  —  36643.55-j-  inches  ;  and  on  this  the 

pyramid  proper  is  constructed. 
The  elements  of  two  are : 
(2.)     Height,  5832       inches,  486        feet. 

—  base  side,  45S0.44       "        38170     " 

2 

—  base  diagonal,  6477.72       "        539-8i     " 

2 

Radius,  6513.47       "        542.78     " 

The  elements  of  three  are  : 
(3.)     Height,  3712.76  inches,  309.39  feet. 

—  base  side,  2916.  "        243.00 


(( 


2 


—  base  diagonal,  4123.84      "        343-^5    " 

2 

Radius,  4146.60      "       345-55    " 

Where  these  elements  are  derived  from  elements  in  (2.)  ;  and 
where  the  height  is  one  of  the  extremes  of  the  geometrical  prob- 
lem, §  74  (3.) 

These  are  the  circles  whence  the  complete  pyramid,  as  to   its 


156  Pyramid  Symbolization.  §  82 

outside^  and  as  to  its  inside^  is  fitly  framed,  and  put  together, 
giving  the  measures  of  the  heavens  and  the  earth. 

The  symbol,  then,  should  be  of  three  circles,  one  within  the 
other,  with  the  triangular  representation  of  the  pyramid  con- 
tained, or  else  a  ■pentagon^  or  the  pentapla  of  Solomon  ;  but  the 
triangle  would  be  more  pertinent.  While  the  triangle  represents 
the  pyramid,  the  triangle  and  circle  represent  the  elements  from 
whence  the  plane  measure  of  the  square^  of  the  base  of  the  pyr- 
amid, is  derived. 

(i5.)  Now  a  tmit  of  measure  is  desirable,  for  translation  of 
geometrical  combinations  of  shapes  into  their  proper  numerical 
equivalents,  for  working  out  the  co-ordination  of  tifjie  with  dis- 
tance relations. 

While  the  two  sets  of  values,  6561  :  20613,  and  113  :  355,  are 
essentially  connected  together,  and  are  in  some  way  but  varia- 
tions on  each  other,  so  that  113  and  355  carry  with  them  by  im- 
plication a  decimal  value,  as  springing  from  6561  to  20613,  yet, 
as  they  stand,  they  bear  a  beautiful  differential  relation  to  each 
other,  as  follows : 

(I.)     6561  :  2o6i3     ::     113  :  355  gi^ 

/     N  r-  ^    r  3061 1 

(2.)     30612  :  61^61   :  '\^K  :   112 — - — 
^    ^  ^  ^^^  20612 

In  this  last  formulation,  the  fourth  term  is  a  dia?neter  or  straight 
line  value;  and,  as  regards  113,  is  seen  to  differ  from  it  by  just 
ofie  unit  as  a  straight  line  (or  diameter  value)  one^  of  the  de- 
nomination of  20612,  the  elements  of  a  perfect  circle  or  cir- 
cumference, and  this  difference  is  implied  in  the  Jehovah 
or  mn*  value,  which,  as  will  be  seen  hereafter,  springs  from  113. 
This  difference  of  i  —  20612  implies  the  entire  pyramid  scheme, 
for  a  right  line^  as  |  or  — ,  signifies  a  solid  unit  or  cube,  whose 
edge  is  |  or  — ,  or  one ;  and  here  the  denomination  of  this  one 
is  20612,  the  perfect  circumference  value,  and  for  original  meas- 
ure taken  as  inches;  therefore,  the  straight  line  one^  or  |  ,  is 
of  the  value  of  an  inch  cubed,  or  is  a  cube  of  an  inch  to  the 
edge.  Take  off  the  value  of  the  20612  onto  the  edges  of  this 
cube,  and  each  edge  (there  being  12)  will  be  of  the  value  of 
1.71766-J-,  which  is  a  reduction  by  scale  of  the  cubit  value  in 
terms  of  the  British  foot.  This  has  been  before  set  forth  ;  the 
diflerence  is  that  here  the  scale  is  reduced  from  the  least  tinit 
measure^  viz.,  that  of  the  inch.  This  reduced  form  of  subdivis- 
ion is  actually  to  be  found  in  the  coffer  measures  of  the  king's 


§  82.  Pyramid  Symboltzation.  157 

chamber,  as,  for  instance,  one  line  of  that  measure,  by  Professor 
Smyth, 

is  90.175  inches. 

Now,  1.717666-f- X  75- =  90.1774     " 
where  1.71766  is  the  cubit  value  reduced  to  the  scale  mentioned. 

Thus  can  be  seen  the  magnificence  of  the  value,  because  the 
exactitude  of  the  Jehovah  diameter  value  lays  in  the  implied  use, 
which  will  derive  di.  perfect^  yet  combined,  unit  value,  which,  as 
seen,  is  |  ,  as  a  straight  line  of  the  denomination  of  20612, 
which  is  an  abstract  ^^r/(7C/  circular  and  circular  area  value. 

(c.)  This  is  shown  to  have  been  the  case  otherwise.  To  ex- 
press this  value  by  symbol,  the  picture  would  be  of  |  as  a  straight 
line  and  a  O  as  a  circle,  or,  together,  10,  which  is  the  perfect 
form  of  one,  and  at  the  same  time  expresses  the  value  of  ten,  or 
10.  With  the  Hebrews,  it  is  kabbalistically  said  that  the  ten  is 
the  one,  and  the  one  is  the  ten. 

"  Kabbala  says :  '  This  number  10  is  the  mother  of  the  soul, 
and  the  light  and  the  life  are  there  united  ;  since  the  number  one 
is  born  from  the  spirit  (in  the  New  Testament,  spirit  is  John  the 
Dove,  and  John  the  Dove,  or  fonah,  by  the  fsh  use,  becomes 
Jehovah),  thus  the  unity  (i)  has  made  the  ten  (10),  and  the  ten 
(10)  the  unity  (i)."     (Hermes  xiv.,  quoted  from  Sod.,  p.  57.) 

The  reason  of  this  definition  can  be  made  obvious.  The 
primal  one  contained  all  the  elements  oi  generation,  and  there- 
fore included  the  male  idea  and  ihe  female  idea  in  itself  Thus, 
I  contained  |  as  a  male,  and  O  (a  circle)  as  a  female,  yet  it  was, 
as  a  primal  conception,  but  one.  But  these  two,  as  separated 
parts  of  one,  arranged  together,  were  10,  or  ten;  therefoi-e,  the 
interrelation  of  i  =  10,  10  =  i.  But,  again,  with  the  Hebrews, 
I  was  taken  by  itself,  under  another  form,  as  combining  in  itself 
two,  i.  e.,  it  was  susceptible  of  division  into  two  parts  which 

I 
should  make  one.,  and  each  of  these  parts  was  necessarily—,  or 

— ,  or  .K,  which  was  the  letter  H,  or  the  wo7nb  letter,  from  whence, 
10 

the  rabbins  say,  God  created  all  things.     But  add  .5  and  .5,  and 

we    have  i  ]  o,  or  the  male  female  again,  or  the  perfect  ofze- 

Again,  this  10,  or  the  perfect  one,  was  denoted  by  the  Hebrew  letter 

♦,  a  sacred  letter,  denoting  the  word   fah  or  fehovah,  meaning 

what  has  been  said  (among  other  things)  ;  for  *  stands  for  i,  the 

male,  and  o,  the  female.     But  o  was  esteemed  (as  female)  to  be 

equal  to  the  word  for  a.  fsh,  taken  asfeffzale,  or  the  letter  ^  raised 


158  Pyramid  Symbolization.  §  82. 

to  another  scale  of  value,  ^,  or  «,  or  from  .5  to  .5  X  10  ^  5.0, 
where  we  have  5  —  o,  or  H  feminine,  and  o  feminine.  Now,  the 
letter  J,  or  «,  was  named,  and  was  the  word  Nun,  oxjish,  or  pj), 
and  its  values  were  565,  which  word  and  values  are  considered 
fcjninine,  because  raised  frotn  a  feminine  source.  But  565,  or 
Jish,  or  womb  of  5  — o,  or  j  (for  .5  or  n)»  is  equal  to  113  X  -5  = 
56.5,  where  113  is  man  (a  straight  line  or  phallus  value)  mul- 
tiplied by  Hi  or  the  womb  value  ;  and  this,  as  seen,  equals  1*)J, 
or  Jish,  or  5  —  o.  Now,  the  eqtiivalent  of  pj,  565,  is  XV\T\i  or 
565,  and  XV\T\  is  "Cae  female  part  of  the  great  word  mUN  or  Jeho- 
vah, which  thus  assumes  this  word  form  as  the  eqtiivalent  for 
the  tnalefemale  uses  above  shown.  But  as  the  parallelism  must 
be  maintained  to  preserve  the  unity  of  the  God-head,  as  male- 
female,  and  yet  its  separated  cortdition^  we  have  the  values,  56.5 
X  10  (as  a  form  to  show  this)  =  565,  where,  by  the  letter  forms, 
for  565.^ ",  we  have  T\'SiV  '■>  JK^A  after  all,  this  amounts  to  56.5  X 
10  ^  565,  by  completing  the  multiplication,  or  reproduces  XV\T\i 
or  the  phallus  is  thus  concealed  in  the  primal  emptiness  or  7ioth- 
ingness,  which  is  Bohu,  "^HD?  or  Muth,  mother,  JlID*  or  Venus, 
or  Eve,  i.  e.,  the  primal  emptiness  out  of  which  reality  sprung: 
(And  this  concealment  is  allied  to,  and  in  exact  harmony  with,  the 
same  idea  in  another  form,  or  word  form,  and  nu?nber  form  com- 
bined, for  \}i\^  flux  word  is  Nun,  pj,  or,  in  itself,  the  female,  as 
fsh.  This  is  O,  and  because  its  value  is  56.5  (113,  matt  X  Si 
woman') ^  it  is  the  equivalent  of  the  samCi  with  '^y\T^^>  which  also 
equals  565.  Thus,  niH  i^  the  female,  by  this  equivalence  ;  but, 
being  so  on  its  word  face,  it  nevertheless  conceals  within  itself 
the  value  113  (because  113  X  5  =  mil)?  which  is  a  straight 
line  or  diameter  value,  or  "  ifiaji^^  and  therefore,  as  opposed  to 
O,  is  male.  Therefore,  the  harmony.)  And  this  shows  that  the 
mother  idea  was,  after  all.,  the  primal  one,  and  that  the  Roman 
Catholic  conception  is  right.  How  exceedingly  beautiful  the 
display  is.  For  while  we  have  the  full  form  niri~*5  ^s  male- 
female,  yet  it  so  springs  that  this  form  is  evanescent,  as  56.5  X  ^  **? 
because,  completed,  the  perfected  form  becomes  TWHi  or  5^5?  the 
10,  or  %  having  vanished  or  concealed  itself. 

(d.)  Then,  here,  we  have  man  ^113  diameter  {phallus')  to  a 
circumference  of  355,  multiplied  by  .5,  or  womb  ==  mn>  the  fe- 
male part  of  Jehovah  ;  and  this,  as  56.5  (or  fsh,  pj)  multiplied 
by  10  equals  56.5  X  10  ^  TX\T]'^i  the  great  name,  which,  after 
all,  is  10,  or  primal  one.  As  seen,  when  113  :  355  is  compared 
with    6561    :    20612,  the  perfect  circular   element,  we  have  to 


§  82.  Pyramid  Symbolization.  159 

1  2061 1    ,1  ,  ,      ,.-- 

make  up  the  ii-^,  as  112 — -^ 7 — =ii'?;  where   the  clif- 

^  ^  20612    '    20613  ^ 

fercntial  is  a  one  straight  line  {jyJiallus')  of  the  denomination  of 

the  perfect  circle  {yoni),  or  20612  ;  and  this  is  thus  seen  to  be 

necessary  to  make  the  113.    But  113  X  '5  ^  5^-5'  ^^  TVST]  ',  thus, 

//  is  also  necessary  to  make  this  value:  but  56.5  X  10  =  TV\TV  '■> 

therefore,  it  is  also  necessary  to  make   tip  this  value.     But  this 

value  is  Jehovah  ;  wherefore,  the  necessity  is  a  straight  line  one^ 

of  a  denoi7ii7tatio7t  0/20612,  or  ihe  perfect  one,  and  jfehovah  has 

been  shown  to  be  this. 

So,  while  jfehovah  expresses  ihi?,  perfect  one,  under  the  Parker 
forms,  through  the  Metius  use  it  also  expresses  a  larger  diameter 
value,  as  565S  derived  from  113  X  -5  =  565,  and  56.5  X  ' '^ 
(=  ,*7"^n»)  =  565,  where  113  is  diameter  to  circumference  of 
355.  The  involution  of  the  Parker  and  Metius  forms  seems  to 
be  in  the  queen's  chamber  in  the  pyramid. 

Besides  this,  the  two  words  of  vvhich  fehovah  is  composed, 
make  up  the  original  idea  of  male-female,  as  the  birth  originator 
(for  the  *  was  the  membrum  virile,  and  Hovah  was  Eve).  So, 
it  is  seen  that  the  perfect  one,  as  originator  of  measures,  takes 
also  the  form  of  birth  origin,  as  hermaphrodite  one;  hence,  the 
phallic  form  and  use. 

So  the  perfect  symbol  is  made  up  of  three  circles — one  within 
the  other — a  triangle  inscribed,  and  in  this  the  word  mUS  as  the 
originating  one  of  all  things. 


As  I  H  S,  or  tJ^n*,  or  (the  values  being  added)  3i8-|-,  it  would 
give  diameter  to  a  circumference  of  one;  and,  therefore,  I  H  S 
is  a  Jehovah  form. 

(c.)     It  would  take  up  too  much  space  to  go  into  particulars  ; 

but  it  could  be    shown  that  the  word  XVXV  should  be  placed  in 

the  darkness,  around   the    borders  of  which    an    intense    light, 

above  the  brightnes  of  the  sun,  should  reside  as  issuant  from  the 

Word.     (Also,  that  in  the  symbol  10,  the  i,  as  another  symbol. 


i6o  Pyramid  Symbolization.  §  82. 

may  be  supposed  to  represent  the  word  John^  and  should  stand 
on  the  'western  or  autum7ial  side  of  the  celestial  circle?)  If,  in- 
stead of  the  word,  a  diameter  line  is  drawn  across  the  circle,  this 
form,  of  itself,  would  be  expressive  of  \ki^  great  word,  and  thus 
the  circle,  with  its  diameter  line,  would  again  express  the  number 
10.  Another,  and  very  beautiful  symbol,  might  be  placed  in  the 
pyramid  triangle,  viz.,  that  of  an  oblongs  or  two  squares,  bearing 
the  form  of  an  open  book  ;  but  this  is  more  appropriate,  as  in- 
cluding the  ark  of  Noah  in  the  pyramid  symbol.  This  figure  is, 
by  cutting  it  in  two,  the  origin  of  the  Hebrew  letters  jf  and  ^. 
The  value  of  H  is  8,  and  that  of  H  is  5.  The  number  5  was  the 
birth  number,  as  its  letter  Hi  its  sign,  was  the  symbol  of  the 
womb.  The  number  8  signifies  the  use  of  5.  In  the  Hebrew 
conception,  everything  made  by  the  Creator  was  a  perfect  one, 
and  by  this  method  was  z.  perfect  cube,  as  one.  But  birth  neces- 
sitates the  two  opposites  of  inale  and  female,  each  of  whom  had 
to  be  in  itself  perfect.  To  combine  these  two  so  that  the  duality 
may  be  preserved,  and  yet  a  perfect  OJie  result^  if  the  originat- 
ing cube  be  used  eight  times,  the  result  is  another  perfect  cube, 
combining  the  two  opposite  or  separated  capacities  for  produc- 
tion within  itself  This  is  exemplified  in  the  family  of  Noah. 
To  make  a  perfect  productive  one,  they  had  to  be  eight;  and  so, 
in  fact,  they  were,  as  they  entered  the  ark.  Now,  the  values,  as 
applied  to  Noah,  would  give  us  his  name  as  HH  (or  8-5,  and  the 
larger  cube  from  5  would  make  one  of  10  to  the  side,  or  a  Jeho- 
vah cube),  whereas  it  is  f^j,  and  for  this  reason :  there  is  no 
change  determined  on  the  value  of  5  (as  H)  by  the  use  of  ^  or  n, 
because  J  is  5  only  enlarged  from  J^,  in  the  ratio  .5  X  10  =  50, 
or  5  X  10  =  50.  The  j,  or  n,  is  used  to  get  \\\e.  fish  letter,  as 
nun,  or  pj,  or  565,  the  Jehovah  form,  as  shown  ;  and  this,  taken 
as  a  cube,  eight  others  make  up  the  equivalent  larger  one,  or  10, 
or  Jehovah.  Showing  the  Noah  glyph  to  be  a  Jehovah  one,  or 
Jah-is  Noah,  or  T\^i  which  is  the  British  inch — that  cubic  one 
above  shown  forth. 

Note  that  this  is  of  great  importance.  Take  the  origin  of  (IJ 
in  nn  ;  this,  by  symbol,  is  8  —  .5,  where  .5  is  a  womb  cube  ;  but 
to  fructify,  it  must  combine  male  and  femple  in  one  ;  so  it  takes  8 
to  make  the  next  larger  perfect  cube,  whose  face  will  necessarily 
be  .5  -|-  .5  =  i.o,  or  a  unit  one.  Jehovah  is  also  a  unit  one. 
Then,  Jehovah  and  Noah  are  equal,  or  one  equals  one;  and,  by 
contraction,  the  expression  of  this  will  be  ^J"^  I-nch,  where  the 
concrete  form  is  "  Jah  (or  Jehovah)  is  (or  equals)  Noah"  or,  to- 


i.  ■''       .    I 


§  '^2>-  Pyramid  Symbolization.  i6i 

gather,  they  signify  I-nck.  If  J  is  taken  for  T],  this  only  changes 
the  value  by  ciphers,  which,  instead  of  enlarging;  can  be  taken 
as  smaller  subdivisions ;  or,  in  fact,  the  ciphers  may  be  dropped 
by  Hebrew  usage.  The  pyramid  is  built  on  the  British  inch,  as 
shown  ;  the  Garden  of  Eden,  etc.,  is  the  expression  of  the  same 
thing  under  another  style  of  setting  forth.  It  seems,  then,  clearly 
evident  that  our  English  word  inch  is,  in  fact,  from  the  combination 
of  the  Hebrew  unit  designations,  viz.,  Jah  and  Noah,  or  (1^"% 
or,  literally,  I-nch. 

The  ark  of  Noah  was,  in  dimensions — 

(i.)     300  X  50  X  30  =  450,000  cubits. 

The  cube  of  .5,  or  the  letter  H?  or  J  (its  equivalent),  is  125  ;  then — 

(2.)     450 --  125  =  3.6,  or  36; 

and  36  =  El-h^  T\)^->  ^^  Elohiiti^  while  125  equals  the  Hebrew 
word  |^{<,  abn,  stone,  or  Peter;  so,  here,  we  run  directly  back 
to  a  Jehovah  use,  and  to  a  factor  base  of  6  X  6  =  36,  and  which, 
as  will  be  shown,  is  the  Garden  of  Eden  form.     So — 

(3-)  360  -^  8,  or  n  =  45» 
the  characteristic  value  of  the  cubical  contents  of  the  ark  itself. 
Once,  again,  the  woman  is  nifl^  and  *  is  the  male — together,  the 
perfect  number  10;  but  10  is  a  circumference  to  a  diameter  of 
318-I-,  and  this,  in  one  form,  took  the  idea  of  the  birth  of  time, 
as  of  ^eyear;  therefore,  in  this  form,  mH^  would  indicate  also 
the  ferfect  year;  and  318  was  a  Christ  value.  As  the  perfect 
year,  the  circle  divided  by  a  horizontal  diameter  line,  would  be 
the  symbol  of  the  perfect  one,  or  ,1111%  while,  to  denote  the  sepa- 
rated functions,  the  upper  or  sunny  half  would  be  ^,  while  the 
lo-voer  half  would  be  the  niH,  or  dark,  or  Eve  portion  of  the  year. 

The  Trowel  Face. 

§  83.  It  has  been  seen  that  the  commencement  of  the 
pyramid  proper  is  by  means  of  placing  an  ideal  pyramid, 
constructed  on  the  elements  of  (i.),  §  82,  in  a  sphere.  The 
results  there  displayed  are  through  geometrical  proportions. 
The  base  of  the  interior  construction  is  seen  to  rest  upon 
the  geometrical  problem  displayed  in  (5.),  §  74.  In  that 
problem,  all  the  pyramid  elements  of  construction  are  dis- 
played ;  for  AB  is  the  standard  base  side  of  the  pyramid, 
C  D  is  the  standard  height,  and  D  B,  with  the  angle  C  B  E, 
are  seen  to  enter  into  the  aggregate  height  lines,  and  the 


i62  Pyramid  Symbolization.  §  83. 

roof  lines  of  the  interior  levels,  and  chambers.  Moreover, 
A  D  and  C  D  are  but  reductions  from  the  original  forms 
as  given  by  Mr.  Parker.  The  shape  of  the  inclosed  figure 
A  C  B  E,  could  be  changed  so  as  to  display  the  exact  pyr- 
amid standard  relations  ;  for  by  doubling  the  line  A  D,  or 
763.4074  X  2  =  1526.8148+,  the  proportion  of  C  D  : 
A  D  X  2  is  that  of  diameter  to  circumference  of  a  circle, 
and  is  the  exact  proportion,  and  in  the  exact  numbers  of 
height  to  twice  the  base  side  of  the  pyramid.  Architectur- 
ally, this  is  valuable  for  symbolization  ;  for  by  doubling  AD, 
and  inclosing  the  extension  by  the  lines  A  C,  C  B,  B  E,  and 
A  E,  the  new  form  displayed  would  be  that  of  the  mason's 
trowel  face :  so  that  a  trowel  constructed  after  these  propor- 
tions, and  on  the  scale  of  the  British  inch,  would  afford  to  the 
mason  the  whole  elaborated  plan  of  his  work  with  the  re- 
lations of  the  elements  from  whence  these  plans  took  their 
rise. 


It  was  an  old  tradition  that  in  the  accomplishment  of  any  great 
and  good  work  involving  the  more  abstruse  and  recondite  knowl- 
edges, the  workmen  would  be  beset  by  the  powers  of  the  realms 
of  darkness,  with  their  frights,  and  horrors,  and  scares.  As 
against  these,  the  master  workman  would  protect  his  work  by  the 
display  of  the  seal  of  Solomon,  the  wise  man,  and  the  king,  even 
over  the  Efreets^  the  yinn,  and  the  Jann.  But  even  here,  he 
had  to  summon  up  an  amazing  amount  of  lesisting  force ;  nor 
could  he  do  this  unless  by  the  assistance  of  the  unseen  powers  of 
light,  of  truth,  and  of  goodness.  As  encouragement  to  the  fail- 
ing power  and  courage  of  the  master  workman,  on  whom  the 
whole  charge  rested,  a  voice,  like  as  the  Bath-Col^  Daughter 
of  the  Voice^  would  come,  in  terms,  like  the  following  which 
were  given  to  Hasan  El  Basrah  in  his  terrible  trials : 
"  I  disposed  thine  affair  at  the  time  when  thou  wast  in  thy  moth- 
er's womb, 
And  inclined  her  heart  to  thee  so  that  she  fostered  thee  in  her 

bosom  : 
We  will  suffice  thee  in  matters  that  occasion  thee  anxiety  and 

sorrow ; 
So,  submit  to  us,  and  arise :  we  will  aid  thee  in  thy  enterprise. 


§  84.  The  Temple  of  Solomon.  163 


CHAPTER  IV. 

THE    TEMPLE    OF    SOLOMON. 

§  84.  Kabbalistic  tradition,  passed  down  in  Succoih, 
states  that  when  Solomon  was  about  to  erect  the  temple,  he 
found  the  measure  wherewith  to  build  it,  by  placing  the  name 
of  'Jehovah^  XXS'sV  ^  upon  th€  round  mouth  of  the  well-hole  in 
digging  the  foundations  ;  and,  again,  it  is  said,  by  placing 
this  name  upon  the  bung-hole  of  a  cask.  The  "  round 
tnoiith  "  and  the  "  bung-hole  "  were  circles.  The  Israelites 
converted  circular  and  spherical  measures  into  square  and 
cubic  measures,  in  their  representations  of  them.  It  will 
be  shown  that  the,  or  one  of  the,  values  of  the  name  "Jc- 
kovah,  was  that  of  the  diameter  of  a  circle  ;  and  it  espe- 
cially meant  the  unit  measure  of  a  right-line,  or  square- 
sur/ace,  or  cube-solid,  having  a  purely  circular  value. 
Hence  the  definition  of  the  architectural  idea  of  construc- 
tion is  thus  conveyed  in  Succoth,  if  this  was  the  channel 
of  the  tradition. 

The  description  of  the  temple  measures  are  to  be  graded 
in  the  following  order  : 

(i.)  From  the  Book  of  Kings.  (2.)  From  the  descrip- 
tion of  the  Tabernacle ;  because  it  was  perfect  in  all  its 
proportions,  and  Solomon  could  do  no  more  than  to  repro- 
duce it,  however  much  he  might  vary  the  style  of  archi- 
tecture. (3.)  From  the  Book  of  Chronicles,  not  so  au- 
thentic, but  rather  a  targum,  or  paraphrase,  on  Kings  ;  and 
(4)  from  Jose^hus. 

The  Details  of  Dcscriptiott. 

(a.)     The  entrance  to  the  temple  faced  toward  the  cast,  ^' 
and  the  holy  of  holies  was  in  the  extreme  west  end. 

As  to  the  ground  plan,  the  description  in  i  Kings,  6,  is 
concise,  plain,  and  specific.  This  ground  plan  has  three 
distinctly  separated  parts  :  (i.)  The  house,  ''Bayith."    (2.) 


164  The  Temple  of  Solomon.  §  84. 

The  temple,  or  open  vault  of  heaven,  before  the  face  or 
door  of  the  house,  ^^Hecal"  (3.)  The  forch  before  the 
face  or  door  of  the  temple,  ^'-Olatim"  Verse  2  says: 
"And  the  house  which  King  Solomon  built  for  the  Lord 
(Jehovah),  the  length  thereof  60  cubits,  and  the  breadth 
thereof  20,  and  the  height  thereof  30  cubits."  Verse  3 
says:  *'And  the  porch  before  the  mouth  or  door  of  the 
temple  of  the  house,  20  cubits  was  the  length  before  the 
face  of  the  breadth  of  the  house,  10  cubits  the  breadth  be- 
fore the  face  (or  door)  of  the  house."  Verse  17  says: 
"And  40  cubits  was  the  house,  that  is  to  say,  hua,  the  tem- 
ple, before  its  face  (or  door)." 

There  is,  then,  the  house,  hayith,  60  cubits ;  the  temfle, 
htcal,  40  cubits;  and  the  length  of  the  -porch,  olaum,  20 
cubits,  one  length  connected  with  another,  for  the  ground 
plan,  or  a  total  length  of  120  cubits.  This  gives,  or  em- 
braces, in  the  house  and  temple  inclosure,  the  length  of  the 
tabernacle  and  court  inclosure,  of  100  cubits.  As  to  the 
porch,  olaum,  in  front  of  the  temple,  2  Chronicles,  chapter 
iii,  verse  4,  says:  "And  the  porch  that  was  in  the  front, 
the  length  was  according  to  (or  agreeing  with)  the  breadth 
of  the  house,  and  the  height  an  hundred  and  twenty 
(120)  cubits,  and  he  overlaid  it  within  with  pure  gold." 
Here,  it  is  observable  that  the  holy  of  holies  was  lined  with 
gold  ;  it  was  at  the  extreme  end  of  the  length  of  120  cubits. 
Here,  the  base  of  the  porch,  or  bottom  of  a  height  of  120 
cubits,  of  the  same  dimensions  as  to  the  length,  and 
one-half  the  width  of  the  most  holy  place,  is  also  lined 
with  gold,  going  to  show  that  the  connection  of  these  gold 
lined  rooms  had  to  do  with  the  distance  of  120  cubits. 
Josephus  says  there  was  a  superstructure  above  the  house 
equal  to  it  in  height  (30  X  2  =  60),  and  then  doubled, 
making  a  total  height  of  120  cubits. 

What  the  inclosure  of  the  temple,  hecal,  part  was,  as 
distinguished  from  the  house,  bayith,  is  not  specified ;  but 
it  is  simply  stated  that  the  door  of  the  house  opened  into 
the  temple  part,  and  the  door  of  the  temple  part  into  that 
oi  the  porch.     It  may  have  been  an  intermediate  court  like 


§  84.  The  Temple  of  Solomon.  165 

the  court  of  60  cubits  before  the  tabernacle  structure  ;  the 
difference  not  being  in  the  sum  of  the  lengths,  which,  in 
either  case,  was  40-|-6o=  100  cubits,  but  in  the  one  case 
the  court  is  40,  and  in  the  other  60  cubits  long.  The  tem- 
ple, likely,  was  a  court  looking  to  the  open  vault  of  the 
heavens,  and  surrounded  by  other  inclosures.  But  what 
became  of  the  altar  of  incense?  Of  the  table  for  show 
bread?  Of  that  for  the  golden  candlestick?  These  sup- 
posed to  be  placed  in  the  most  holy  place  before  the  vail, 
as  in  the  tabernacle,  then  the  only  further  change  of  ar- 
rangement seems  to  have  been  simply  in  the  location  of 
the  brazen  sea  in  the  northeast  corner  of  the  house  inclos- 
ure,  part  of  the  court  before  the  tabernacle,  now,  or  here, 
placed  under  roof;  the  great  brazen  altar  being  located  be- 
fore the  house  in  the  temple  part.  2  Kings,  16,  14,  men- 
tions this  as  in  the  forefront  of  the  house,  and  this  is  again 
implied  in  i  Kings,  8,  64.  It  could  not  be  located  within 
the  house,  as  there  would  be  no  space  around  it.  This 
fact  of  its  being  before  the  house,  gives  a  distance  between 
the  house  and  the  porch,  as  the  temple  part,  i  Kings,  6, 
says  that  there  were  two  ■pillars — Jachtn,  which,  according 
to  Josephus,  was  on  the  south  side,  and  Boaz,  which  was 
on  the  north  side  of  the  porch  entrance.     They  were  18 

I 
cubits  in  height  each,  or,  together,  36  cubits,  or  the  — 

of  360° ;  and  they  girded  12  cubits. 

The  holy  of  holies  was  a  cube  of  20  X  20  X  20  cubits, 
located,  as  stated,  in  the  west  end  of  the  house,  bayith. 
Five  colors  seemed  to  be  involved  about  and  in  it.  It 
was,  according  to  Josephus,  built  in  ivhite^  or  the  color  of 
the  ether.  Inside,  it  was  lined  with  red  cedar.  This, 
again,  was  lined  with  orange  gold.  The  interior  was 
closed  against  light,  and  was  in  the  blackness  of  darkness, 
as  the  proper  place  for  the  ark  of  the  covenant  (or  the  meet- 
ing together  of  two  opposite  principles).  It  is  thought  that 
these  colors  were  typical — red,  of  the  earth  ;  golden,  of  the 
sun  in  general,  or  the  sunny  part  of  the  year,  when,  or  as, 
contrasted  with  the  brazen  sun  of  winter ;  white^  or  silver 


i66        The  Temple  of  Solomon.        §  84. 

color ^  of  the  moon  :  and  black,  of  the  night,  of  the  womb, 
of  the  nadir.  The  condition  of  the  room  as  to  colors  would 
seem  to  indicate  time  and  earth  measures,  and  also  the 
place  where  those  earth  measures  were  to  be  found,  or  to 
be  originated,  as  down  in  the  depths  at  the  center  of  a  mass, 
in  the  dark ;  like  finding  a  starting  point  of  construction 
by  placing  a  pyramid  in  a  sphere. 

(3.)  The  holy  of  holies  was  divided,  as  to  its  cubical 
contents,  by  the  placing  of  the  cherubims.  There  seems 
to  be  no  especial  meaning  to  this  word,  fitting  it  for  such  a 
place.  The  meanings  usually  assigned,  though  perhaps 
proper  enough,  after  a  fashion,  as  man,  angel,  cherub,  are 
really  not  proper  to  the  term.  The  word  comes  from  !l*ll!) 
=  Carab,  or  Carab,  meaning  -prehensile,  to  seize,  grasp 
as  -with  talons,  or  between  talons  ;  as  substantive,  it  means 
a  bird  (as  a  griffin  or  eagle),  fierce,  because  of  its  quality 
of  closing  upon  something,  or  anything,  with  its  talons. 
It  is  the  British  word  crab,  that  seizes  with  its  circular 
pincers  ;  also  the  word  grab,  as  closing  the  fingers  upon 
something.  On  looking  at  the  zodiac  signs  for  yune  and 
aV  October,  it  will  be  seen  that  they  are  represented  as  closely 

alike — one  as  the  scorpion,  and  the  other  as  the  crab ;  and, 
in  fact,  for  the  zodiac,  these  two  answered,  as  stretching 
over  or  embracing  the  two  cubes  representing  that  quad- 
rant of  the  year  between  cancer  and  scorpio,  just  as  the 
cherubims  stretched  over  and  embraced  the  covenant  or 
meeting  of  the  two  halves  of  the  ark.  This  word  is  es- 
pecially used  as  to  the  Garden  of  Eden,  guarding  the  way 
to  the  tree  of  life  in  the  center  of  the  space,  the  place  of 
covenant  or  o(  meeting.  In  one  sense,  they  may  be  taken 
as  the  hooks  barring  the  opening  of  the  sistrum.  It  is  used 
as  spanning  half  the  space  over  the  ark  of  the  covenant; 
and  the  same  use  is  here  made  as  for  each  one  spanning 
half  the  space  over  10  cubits.  The  real  value  of  the  word 
is  thought  to  be  /;/  its  numerical  value,  which  is  D  =  20, 
^  ==  200,  ^  —  2,  or  a  total  of  222.  These  cherubims  were 
10  cubits  in  height,  and  stood  with  outstretched  wings  of  5 
cubits  in  length, 'each  touching,  as  to  each,  the  wall  upon 


§  84.  The  Temple  of  Solomon.  167 

one  side,  and  the  tip  of  the  wing  of  the  other,  in  the  midst. 
Underneatii  the  meeting  or  covenant  of  the  wings  was  the 
division  line,  either  of  separation  or  of  meeting  of  the  two 
rectangular  solids  of  the  ark  of  the  covenant  (signifjdng 
the  two  sexes). 


Comparison   of  the  Afcasures  of  the   Tcmj^le  zvith  those 

of  the  Pyramid. 

{c.)  (i.)  As  to  the ////«r5.  18  cubits  =  20.612 -|- 10.306 
feet,  or  30.918  feet;  and  these  are  the  numerical  values, 
divided  by  10,  to  give  the  standard  measures  of  the  vertical 
axial  line  of  the  pyramid,  to  embrace  the  distance  be- 
tween the  top  of  Campbell's  chamber  and  the  base  of  the 
pyramid,  and  between  the  base  and  subterranean  (§  78). 

30.918  ^  — =25.765,  and — the  length  of  the  ark  is  25.765 
12  2 

inches.  The  girth  of  the  pillars  was  12  cubits  =  20.612 
feet,  showing  that  the  circumference  was  in  terms  of  a  per- 
fect circumference  value.  Whether  the  sum  of  the  heights, 
or  36,  was  to  represent  a  reduction  of  the  circle  of  360°,  is 
a  matter  of  conjecture ;  but  it  is  strengthened  by  the  fact 
that  Boaz  was  the  representative  of  Typhon,  or  the  North., 
or  the  dark  or  winter  part  of  the  year,  and  fachin  was  the 
opposite,  and  as  a  division  of  the  standard  circle  of  360°,  each 
would  indicate  the  half,  or  180° :  and  they  are  each  noted 
as  18.  If  the  conjecture  is  right,  one  entered  the  temple 
through  the  gateway  of  the  birth  of  the  year  circle.  This 
is  perfectly  paralleled  by  the  qualities  of  the  descending 
passage-way  in  the  pyramid,  as  it  involved  both  the  circu- 
lar elements  and  their  application  to  the  measures  of  the 
earth  in  its  equatorial  value  of  360°,  by  its  diameters  in 
miles,  and  then  the  measures  of  the  time  circles  about  the 
sun  made  by  this  very  equatorial.  As  to  these  applications, 
see  §  72.  This  view  is  partly  confirmed  by  the  name  given 
to  the  location,  or  olaum,  or  porch  ;  for,  by  the  interchange 
of  ^^  for  ^,  and  this  is  rulable,  this  may,  as  q^ij^  for 
qS«)j;,  be  taken  for  the  otherwise  similar  word  which  means 


i68  The  Temple  of  Solomon.  §  84. 

time  without  end,  eternity,  revolving  ti7ne,  or  Aeon,  or 
Age.  "The  Oidoniini  {Aeons),  Yq\q.q.,  and  Spirit,  and 
word."  ( Jetzira,  9,  10).  "  The  fools  did  not  know  that 
the  Aion  (Aeon,  age)  is  not  any  essence  {pusia)  existing, 
but  some  division  indicative  of  time."  (Theodoret  Haeret. 
V,  vi.).  Wisdom  says  :  "  I  was  effused  from  Oulaum  (Aeon, 
time),  from  the  beginning,  from  the  earliest  time  {mi- 
hadmi)  of  the  earth."       (Proverbs   viii,  23.)      (All  from 

Sod.  p.  76.) 

12 
(2.)     T\vQ.  forch  was  120  cubits  high,  or  206. —  feet,  that 

so  familiar  value  of  the  pyramid.    It  w^as  20  cubits  long,  or 

34*3533+  f'^^t,  or  the  standard  length  of  the  king's  chamber 

in    the    pyramid.     It  was  10  cubits  broad,   or  17.1766+ 

12 

feet,  or  206.  — inches,   the  standard  width  of  the  king's 

chamber.      (3.)  The  -porch,  temple,   and   house   lengths, 

12 
together,  were  120  cubits,  or  206.      'feet,  also;  while  the 

holy  of  holies  plus  the  most  holy  place,  or  40  cubits  in  all,  or 
68.7064  ft.,  was,  as  to  measure,  and  comparative  location,  the 
veritable  measure  of  the  king's  chamber  region,  with  respect 
to  its  like  location  in  the  120  cubit  height  in  the  pyramid. 
(4.)  The  temple  and  house  lengths,  together,  or  60 -|- 40 
=  100  cubits  =  171.766+  feet,  or  2061.2  inches,  was  that 
beautiful  proportion,  as  extending  from  the  base  of  the 
pyramid  to  the  point  C,  marking  the  center  point  of  the 
king's  chamber  region  (refer  to  §  78).  From  the  base  of 
the  pyramid  to  A  is  137.509  +  68.7066=206.12  feet,  or 
120  cubits  (taken  at  the  standard  measures).  The  king's 
chamber  region  taken  from  the  point  C,  with  a  radius  of 
34-3533+  f'^^t,  is  68.706  feet,  or  20  cubits  x  2  =  40  cubits. 
There  can  be  no  mistake  as  to  the  sameness  of  intention  as 

12 
regards  these  like  measures.     (The  value    206.       feet,  or 

120  cubits,  was  a  great  governing  measure,  and  as  it  im- 
plied also  the  full  numerical  value  20612,  being  constructed 
from  it,  it  was  the  great  number  and  value,  after  all,  of 
all  construction,  as  is  fully  set  forth  in  this  work.  This 
number  of  120  cubits,  then,  thus  composed,  is  206,  and 


§  84.  The  Tempi.e  of  Solomon.  169 

its  use  thus,  and  in  its  original  term  of  20612,  is  implied 
in  the  great  measuring  word  throughout  Scripture  and 
Kabbala.  That  word  is  Dabvar,  "1^1,  or  206,  and  is  the 
Logos  word.) 

(5.)     The  holy  of  holies^  as  a  cube  of  20,  was  ji^st  ^ 

of  the  cube  of  the  king's  chamber  region  in  the  pyramid, 
or  the  full  cube  of  the  length  of  the  king's  chamber.  (This 
use,  emblematically,  is  referred  to  elsewhere  ;  but  it  is  of 
so  curious  a  nature  that  it  is  well  to  state  it  again.  The 
primal  one,  or  cube,  was  taken  as  containing  all  material 
and  all  life  within  itself.  It  was  male-female ;  but  when 
disintegration  took  place  of  the  one  into  two  separated  and 
opposed  existences,  as  oi  male  ixnd  female,  each  had  to  be 
a  perfect  one,  also,  in  its  special  construction.  To  make, 
therefore,  z. -perfect  one,  which  will  combine  these  opposed 
relations,  they  are  to  be  used  together,  and  it  requires  just 
8  of  the  smaller  cubes,  viz.,  4  males  and  4  females,  to- 
gether to  make  the  larger.  The  king's  chamber  regioii  is 
the  great  cube  of  this  union ;  and  the  king's  chamber,  as 
to  its  length  of  20  cubits,  was  the  eighth  part  of  the  whole 
cube,  and,  of  itself,  was,  as  to  its  length,  an  oblong  of 
two  cubes,  or,  in  itself,  male-female.)  The  division  by  the 
cherubims  divided  it  into  halves,  making  a  nearer  approxi- 
mation to  the  king's  chamber  proportions.  The  ark,  though 
similarly  a  small  rectangular  solid  or  oblong,  placed  in  the 
holy  of  holies,  as  the  cofter  was  in  the  king's  chamber,  was 
differently  proportioned,  showing  a  difference  of  use  in 
measurement. 

(6.)  As  to  colors,  the  white,  and  red,  and  black  of  the 
temple  tallietl  with  the  like  of  the  pyramid,  the  golden 
being  an  exception. 

(7.)     As  to  the  ark,  it  was  2-   cubits   long,  or  51.53 

inches,  or,  numerically,  the  area  of  the  circle  inscribed  in 
the  square  of  6561.  Its  height  added  to  its  breadth:^ 3 
cubits,  or  5.153 /<:(?/;  showing,  for  one  thing,  that  it  was 
so  contrived  as  to  be  reducible  back  to  the  elements  whence 


170  The  Temple  of  Solomon.  §  84. 

its,  and  all  the  temple  measures,  were  derived  ;  and  this 
could  not  be  done,  by  possibility,  except  by  the  intervention 
of  two  grades  of  measure,  and  those  were,  respectively, 
the  British  inch  and  foot. 

(8.)  But  the  sameness  of  relations  of  the  temple  with 
those  of  the  pyramid  seems  to  be  confirmed  by  the  use  of 
the  cherubims.  They  were  10  cubits  high,  and  by  their 
use  marked  out  the  division  of  the  holy  of  holies  into  10 
cubit  measures.     Take  some  pyramid  developments  : 

(i.)     5153  X  8^41224  inches^  the  circumference  of  the 

base  of  the  pyramid  placed  in  the  sphere. 

206.12 
(2.)     5153  X  2  =  20612.  =  17.17666  feet,  or  10 

42 
cubits.     17.17666  X  -^  =  3053+  feet,  or  36643.55  inches, 

or  the  circumference  of  the  base  of  the  pyramid  proper. 

o  this  circumference  is  381.7037-I-  feet,  or, 

222.222+  cubits. 
//  is  thus  seen  that  the  use  of  the  10  cubits  value  devel- 
ops the  —  base  side  of  the  great  pyramid  in  the  measure  of 

112  cubits.  It  is  seen  that  in  the  development  of  the  holy 
of  holies,  the  ark  contains  the  original  measures.  It  is 
placed  in  a  space  of  10  cubits.  This  10  cubits  measure  of 
division  is  made  by  the  use  of  the  3*15,  or  cherub,  and  the 

numerical  value  of  cherub  is 

222. 


There  is  a  most  strange  and  far-reaching  value  connected 
with  this  cubit  value  of  444.444  for  the  base  side  of  the 
pyramid.  The  4  sides  would  equal  1777-777+  cubits.  The 
pyramid  was  constructed  from  that  value  of  the  Parker  el- 

42 
ements  of  20612  X  -5  =  36643.55+  for  circumference  value, 

42 
and  6561  X  ^=  1 1664  for  diameter  value,  or  for  height. 

Now, 


§84- 


The  Temple  of  Solomon 


171 


(I.)  36643.55  ^  20.612  =  i777-77»  and 

(2.)  11664.  -i-   6.561=1777.77; 

or,  numerically,  this  very  pyramid  base  value.     This  is 

42  42 

brought  about  by  the  factor  -^as  common  to  both.     ~= 

16 

—  ;  and,  as  was  shown,  this  expression  embraces  the  fac- 
tors of  the  square  foot  British,  because  16  X  9  ^  144-  The 
reverse  use  or  16  -=-  9  =  1777. 777+,  showing  that  these  fac- 
tor numbers,  by  another  change  of  use,  at  once  lay  the 
foundation  of  the  pyramid  and  temple  works ;  the  knowl- 
edge of  the  scales  of  measure,  and  the  use  as  applied  to 
geometrical  elements,  being  implied.  Somehow,  all  the 
systems — Hmdu,  Egyptian ^  Hebrew,  2ind  British — belong 
to  one  another,  and  are,  in  fact,  one  system. 


So,  here  in  this  temple,  and  its  holy  of  holies,  and  its 
ark,  we  have  the  ear-marks  of  the  full  use  of  the  pyramid 
measures,  under  another  style  of  architecture.  Was  there 
ever  such  a  concordance  of  measures,  unless  attended  by  a 
similarity  of  use? 

{d.)  The  representation  of  the  holy  of  holies,  in  verti- 
cal cross  section,  is  as  follows  : 


Red 

G ol  tl^n 
Blaek. 


tJachln. 


The  ark  was  the  residence  of  Jehovah,  and  he  specifies 
his  place  as  at  the   meeting  of  the  cubes  of  the  ark,  be- 


172  The  Temple  of  Solomon.  §  84. 

tween  the  cherubims.  What  was  his  numerical  essential, 
to  accord  with  all  these  measuring  properties?  He  was  the 
perfect  one,  or  i — O,  or  a  straight  line,  one,  of  a  denom- 
ination of  the  perfect  circle,  O — viz.,  20612;  reduced 
evenly  and  by  scale,  to  an  inappreciable  minuteness,  not 
to  be  seen  by  the  eye,  nor  conceivable  by  the  senses,  yet, 
nevertheless,  this  -perfect  one. 

Kabbalistic   Matters    Connected   with    the    Temple   De- 
scription. 

[e.')  The  astronomical  features  about  the  temple  were 
plain.  The  entrance  was  toward  the  rising  sun,  or  the 
vernal  equinox.  The  holy  of  holies  was  in  the  west  of  the 
structure,  toward  the  place  of  the  setting"  sun ,  the  autumnal 
equinox.  The  great  quadrangular  was  oriented  and  faced 
to  the  four  winds,  or  N.,  E.,  S.,  and  W.  The  brazen  sea 
had  on  its  ledges  the  ox,  the  cherub  or  man,  and  the  lion. 
The  lion  was  the  sign  of  the  summer,  the  man  of  the  win- 
ter, and  the  ox  of  the  spring.  The  sign  of  autumn,  or 
Dan,  was  left  out — that  worm  all-devouring,  never-dying, 
the  scorpion.  This  has  an  architectural  parallel.  Nork 
relates  that  the  temple  oi  Notre  Dame,  in  Paris,  was  form- 
erly a  temple  of  the  goddess  Isis,  or  the  sign  Virgo.  On 
this  temple  was  sculptured  the  zodiac  with  its  signs ;  that 
of  Virgo  [Isis)  was  left  out,  because  the  whole  temple  was 
dedicated  to  her.  So  with  the  temple.  The  whole  relig- 
ious cultus  of  the  Israelites  was  located  in  the  sign  Dan,  or 
Scorpio,  for  it  was  here  that  "  I  have  waited  for  thy  salva- 
tion, O  Lord  [fehovah).'"  Under  another  form,  Scorpio 
was  the  gate  of  the  woman,  for  it  was  the  door  of  the  eve- 
ning,  or  darkness.  In  Genesis,  God  says  of  the  evening, 
or  darkness,  that  it  should  be  called  Lilah,  Prefix  the 
letter  D,  or  hieroglyph  of  a  door,  and  there  results  D-lilah, 
or  '■^  Door  of  darktiess,"  or  gate  of  the  woman,  or  the 
place  of  the  new  conception — that  gate  into  which  Sam- 
son, as  the  sun  shorn  of  his  beams,  his  7  golden  locks, 
type  of  the  7  sunny  or  prolific  months,  had  to  enter  in  the 
autumn  of  the  year.     It  is  said  that  anciently  the  signs 


§  84.  The  Temple  of  Solomon.  173 

Virgo  and  Libra  were  somehow  held  as  one ;  then  there 
would  run  the  three  months  of  July,  August,  and  Septem- 
ber, as  embraced  between  the  signs  of  Cancer,  the  crab, 
and  Scorpio — that  is,  Leo  and  Virgo,  or  the  male-female, 
would  be  embraced  between  the  two  similar  creatures,  the 
crab  and  scorpion,  or  between  the  two  cherubims,  just  as 
were  the  two  cubes  of  the  holy  of  holies.  Water  was  a 
female  element  sacred  to  the  womb,  or  producing  power. 
"Born  from  the  womb  upon  a  flood."  Brass  was  a  metal 
symbolizing  the  nether  world,  or  the  winter  sun,  or  the 
darkness  of  the  year,  which  was  that  of  the  womb  where 
life  should  be  given  to  the  new  year.  The  recurring  year 
was  symbolized  by  a  serpent  swallowing  (one  or  more  units 
of  its  length)  the  end  of  its  tail ;  and  thus  was  a  female 
emblem  as  reproducing  itself.  The  word  for  serpent  was, 
in  Hebrew,  Nahash.  But  this  is  the  same  term  for  brass, 
and  has,  also,  these  singular  meanings  in  this  connection  : 
"Properly  the  firm,  hence  the  basis,  ground-suf fort'  oi 
the  bottom  of  a  kettle  standing  on  the  fire ;  figuratively, 
the  female  ■pudenda.^''  The  brazen  sea  was  Typhonic 
then.  The  brass  works  belonged  to  Dan,  who  held  the 
gate  to  the  depths  of  darkness.  All  this  is  conveyed  in  the 
description  of  the  building  of  the  temple.  Take  the  two 
squares  of  the  zodiac,  representing  two  quarters,  or  quad- 
rants, of  the  year ;  one  lorded  over  by  Leo,  the  lion,  next 
to  the  summer  solstice,  and  then  going  west  and  down- 
ward, the  second  quadrant  is  reached,  extending  to  the  win- 
ter solstice,  and  lorded  over  by  Dan,  the  scorpion,  who 
holds  the  entrance.  This  upper  square,  or  cube,  is 
golden,  the  male,  full  of  the  fructifying  power  of  the 
sun  ;  the  lower  one  is  the  female,  and  black,  the  womb,  the 
brazen  part.  Now  it  will  be  seen  that  Solomon,  the  son 
of  David,  of  the  tribe  of  Judah,  whose  sign  was  the  lion, 
made  all  the  gold  work.  But  it  was  Huram  that  made  the 
brazen  sea  and  all  the  brass  work.  Who  was  Huram  ? 
The  son  of  a  widow,  a  woman  of  dark  or  black  weeds,  of 
the  tribe  of  Dan,  whose  sign  was  the  Scorpion.  He  made 
the  work  pertaining  to  his  portion  of  the  zodiac — that  is. 


174  The  Temple  of  Solomon.  §  84. 

the  place  of  Typhon,  of  winter,  of  darkness,  of  woman, 
of  the  womb,  etc.  So,  here  is  represented  the  western 
half,  and  the  summer  and  winter  quarters  of  the  celestial 
sphere,  squared,  or  cubed.  Hur  is  the  same  with  mount 
Hor,  as  opposed  to  Mt.  Sinai,  where  the  two  mountains 
represent  the  same  types  as  above,  under  the  forms  oi  fire 
and  cold.  This  same  figure  is  attached,  also,  to  the  build- 
ing of  the  tabernacle.  Touching  the  male  and  female 
cubes,  the  name  mn%  as  embracing  both,  is  also  male  and 
female  in  his  name,  the  two  being  married.  Separated,  ♦, 
is  the  phallus,  and  mil  is  Eve^  or  the  womb,  or  the  dark- 
ness, or  brass,  or  serpent.  Separated  so  as  to  be  distinct, 
and  mn  becomes  widowed,  or  a  widow,  with  a  right  to 
weeds  as  dark  as  the  blackness  of  the  depths  which  her 
quality  represents  (yet  cunningly  enough  carries  the  ♦  con- 
cealed). The  year,  personified  by  the  sun,  was  as  God, 
supposed  to  be  thus  married,  but  at  Scorpio  the  worm  was 
represented  as  separating  the  male  from  the  female  parts, 
whereb}''  one  and  the  female  part  of  the  deity,  going  down 
to  her  own  -place  of  the  dark  womb,  into  the  waters,  be- 
came, as  brazen  rays,  or  rays  deprived  of  the  golden  fruc- 
tifying power,  widowed.  And  thus  the  astronomical  types 
are  expressed.  This  double  cube,  red  as  representing 
the  earth,  seed  measure  of  construction,  should  be,  one 
black,  and  the  other,  white;  and,  in  fact,  the  earth  was 
supposed  of  itself  to  be  made  up  of  like  double  cubes,  fitly 
framed  and  matched,  to  its  full   and  just  proportions. 

Solomon,  who  built  this  structure,  was  the  son  of  David, 
who  was  the  son  of  Jesse.  In  Hebrew,  this  word  is  *tJ^*,  or 
ISI.  In  Hebrew,  the  word  V,  or  being,  existence,  is 
puncted  so  that  in  English  it  reads  Jes.  From  this  V  was 
derived  ♦C^*,  or  Jesse,  and  this,  in  the  New  Testament,  is 
the  Hebrew  name  of  Jesus.  The  English  word,  and  the 
Greek  translation,  is  Jes,  with  the  idiomatic  suffix  us,  and 
eus,  not  belonging  to  the  word.  In  many  cases,  and  in 
many  manuscripts,  this  word  V^ ,  Jcs,  is  written  C^^X,  aish, 
man,  from  the  form  \^^,fire.  There  is  but  little  doubt  but 
that  all  these  words  are  organically  and  generically  the 


§  84.  The  Temple  of  Solomon.  175 

same.  The  implication  is  that,  while  man  is  a  being,  he 
is  also  of  the  primary  jlame^  or  fire.  Carried  to  the  ex- 
tremes of  meaning,  and  Jesus,  as  God  in  the  personifica- 
tion of  man,  was  also  the  highest  essential  fire,  which,  by 
parallelism  from  the  spiritual  to  the  real,  in  the  material 
world,  is  the  sun  in  the  heavens.  While  the  derivation  is 
good  as  y«-us  from  t^%  the  other  was  a  positively  intended 
alliance  in  the  name,  by  the  framers  of  the  New  Testament, 
because  by  them  he  is  called  ^'-  son  ofijnan,"  the  Ben  Enosh 
of  Daniel,  and  son  of  Seth  ;  and  this  necessitates  the  other 
form  of  derivation.  ''Son  of  man""  was  Enosh,  {i^1y^?, 
and  in  this  name,  as  relates  to  the  fire  and  sii7i  meaning, 
there  is  a  determinative  enforcement,  for  the  letter  values 
read  365 — i,  or  the  phases  of  the  solar  year. 

There  is  something  peculiar  as  to  the  opening  of  the  6th 
chapter  of  i  Kings  :  "And  it  came  to  pass,  in  the  four  hun- 
dred and  eightieth  year  after  the  children  of  Israel  were  come 
out  of  the  land  of  Egypt,  in  the  fourth  year  of  Solomon's 
reign  over  Israel,  in  the  month  Zif,  which  is  the  second 
month,  that  he  began  to  build  the  house  oi  {Jehovah)  the 
Lord."  The  chronological  date  here  pointed  out  has  been 
a  very  great  vexation  and  stumbling-block  to  commentators. 
It  is  generally  looked  on  as  a  date  falsely  taken.  But  it  is 
well  enough  a  determination  of  the  meaning  of  the  struc- 
ture which  was  about  to  be  built,  for  480-1-4  +  2=486, 

which,  in  feet,  as  coming  from  6561  X  — ■=  11664  inches, 

was  the  height  of  the  great  pyramid,  or  sun  measure,  the 
interior  works  of  which  were  copied  after  in  the  temple, 
as  has  been  shown. 


APPENDICES. 


The  ancient  kno^vledge  will  again  abound,  and  overflow,  as  water, 
upon  the  earth.  The  remains  of  this  knowledge  are  everywhere  about  us, 
in  cvery-day  use,  and  ^perfect.  Its  revival  will  point  to  the  restoration  of 
the  period  prior  to  the  conficsion  of  lip.  The  prophet  saw  a  valley  filled 
with  a  confusion  of  dry  bones ;  but  the  bones  were  perfect  and  all  there  : 
so  with  us  are  the  vestiges  of  this  knowledge.  At  the  tvord,  bone  came  to 
its  bone;  the  perfect  framework  of  the  ma7i.  "And  he  said,  son  of  man, 
can  these  bones  live.?  .  .  and  behold  a  shaking,  and  the  bones  came  to- 
gether, bone  to  his  bone  :  .  .  Then,  thus  saith  the  Lord  God;  come  from 
the  four  zvi?ids,  O  breath,  and  breathe  upon  these  slain,  that  they  may 
live."   This  is  coming  to  pass.     Then  shall  the  people  know  HIH^ 


INTRODUCTION  TO  APPENDICES. 

§  85.  It  is  claimed  that,  in  and  under  the  letters  and 
words  of  the  narrative  form,  the  Books  of  the  law  of 
Moses,  as  the  foundation  of  the  whole  Bible,  contain  the 
same  cosmical  developments  with  the  pyramid,  and  that  by- 
means  of  numerical  values ;  that  this  is  enforced  in  illus- 
trative and  determinative  ways  by  the  narratives,  and  by 
the  hieroglyphic  values  of  letters  and  words  running  par- 
allel with  the  narratives,  but  by  change  of  meaning  point- 
ing to  and  determinating  the  cosmical  lessons,  or  exact 
problems;  that  while  the  three  ways — viz.,  narrative^ 
mathematical,  and  hieroglyphic— -Z-xq  diverse  from  each 
other,  yet  they  all  display  themselves  without  harm  to  each 
other,  in  its  special  way  or  sense  :  that  is,  the  narrative 
may  be  true,  the  mathematics  may  be  well  taken,  and  the 
hieroglyphic  reading  may  be  exactly  defined  and  true  to 
its  scope.  While  this  is  so,  each  method  may  in  some  sort 
help  the  other,  by,  in  some  way,  setting  it  forth. 

The   Opening  Sentence  in   Genesis, 
(a.)     The  first  sentence  in  Genesis  is. 

It  must  be  borne  in  mind  that  in  the  scroll-reading  the  let- 
ters are  not  separated,  but  run  together,  without  point  di- 
visions, from  which  fact  there  are  two  readings  to  this 
sentence,  as  follows  : 

(i .)     B'rashith  bara  Elohim  eth  hashamayim  v'eth  h'arets. 

(2.)  B'rash  ithbara  Elohim  eth  hashamayim  v'eth  h'arets. 
where  the  verbal  dara,  to  create,  instead  of  the  per/cct  of 
Kal,  may  be  thrown  into  the  third  person  sin gn] ar  yut tire 
of  hithpacl:  (This  reading  pointed  out  by  Rev.  Dr.  Ju- 
lius Goldammer.)     The  translation  of  this  sentence  is,  "  In 

the  beginning  God  made  the  heavens  and  the  earth  ;"  and 

(179) 


i8o  Introduction  to  Appendices.  §  85. 

this  is  the  narrative  form  of  the  sentence.  Suffering  a  closer 
analysis,  this  narrative  form  assumes  a  cosmical  interpreta- 
tion, thus  :  "  ^"  is  a  prepositional  prefix,  signifying  in  the 
largest  sense  in,  and  with  material,  carrying  the  idea  of 
in,  or  out  of,  ox  from,  as  of  material.  Rash  =  head,  and 
is  a  masculine  noun,  but  here  used  with  a  feminine  termi- 
nation, it  signifies  with  the  prefix  and  the  terminative,  "/« 
the  substance  of,''  or  "  out  of  the  head,  as  a  material,  or 
essential.'"  Elohim  is  a  compound  made  up  of  El,  a  mas- 
culine singular,  meaning  the  all-embracing  God ;  to  this 
n,  or  h,  is  added,  as  separating  the  elements  of  El,  and  out 
of  them  constituting  El-h,  or  male  diVid  female.  It  is  the 
compound  of  two  characteristics,  involving  the  use  of  two 
offosites  from  whence  to  mold,  as,  in  sexes,  the  duality 
of  man  and  woman  ;  as,  in  forces,  the  duality  as  centripetal 
and  centrifugal — for  example,  electricity  combining  two 
opposites  under  the  manifestation  of  modification  of  one 
initial  force.  To  this  El-h,  thus  combining  these  two  op- 
posites, a  plural  termination  is  added,  indicating  the  two  in 
combination,  thus,  '■^  God  in  the  {assumed)  double  relation 
of  two  opposites.'"  Then  follows,  not  "  they  created, ""  as 
of  gods,  but  ''He  created:'"  and  then,  not  the  heavens,  as 
we  laxly  take  it,  but  "  the  two,  or  duplex  heavens;''''  for 
in  Hebrew,  from  the  force  of  a  double  construction,  the 
term  is  dual,  not  singular.  So  the  sentence  reads,  "In  (or 
out  of)  his  own  essence  as  a  womb,  God,  in  the  manifesta- 
tion of  two  opposites  in  force,  created  the  two  heavens,  and 
the  earth,"  as  to  the  heavens,  the  upper,  or  light,  and  the 
lower,  or  dark;  signifying  the  opposites  of  heat  and  cold, 
day  and  night,  expansion  and  contraction,  summer  and 
-winter;  in  short,  the  all-embracing  cosmical  relations. 

By  this  reading,  a  mere  meaningless  abstract  enuncia- 
tion assumes  a  general  form  of  shadowing  forth  the  ineans 
and  use  by  which  creation  was  effected. 

Its  Parallel  Numerical  Reading. 
(3.)     Now  comes  the  basis  of  a  more  specialized  and 
exact  reading,  yet  supported  by  the  narrative  style  and  the 


§  85.  Introduction  to  Appendices.  181 

closer  reading.  Referring  back  to  §  34,  there  is  shown  the 
great  use  of  the  differential  El,  as  31,  to  link  together  cir- 
cular with  plane  measures,  all  of  wliich  are  turned  to  cos- 
mical  uses  ;  for,  taking  the  limits  of  the  British  measures, 
and  diffe7'cntiating  hy  EL  or  31,  we  have 

(I.)     144  — 31--113  5184— 3i  =  5i53» 

thus  introducing  two  bases  of  relation  of  diameter  to  cir- 
cumference. Now,  El  is  the  first  god-name,  and  the  great 
working  number  31  ;  and,  by  parallelism,  in  the  construc- 
tion of  the  pyramid  interior  works,  where  the  cosmical 
enunciations  are  made,  the  starting ^oint  is  the  intersection 
of  the  floor  line  of  the  descending  passage-way  with  the 
exterior  slope  line  of  the  outside  of  the  structure,  and  on 
this  starting  point  all  else  interiorly  is  made  to  defend. 
Now,  it  is  seen,  §  64  (2),  that  this  point  of  opening  into  the 
interior  is  located  at  a  vertical  height  of  31  cubits  ;  the  31 
thus  beinor  the  starter  number  of  the  entrance.  But  this 
being  so,  the  dimensions  of  the  descending  passage-way 
depending  on  this  point,  are  seen  to  be,  §  72  {c),  a  combi- 
nation to  iret  a  mean  between  diameter  of  i  to  a  circumfer- 
ence  of  314,  and  a  circumference  of  i  to  get  a  diameter  of 
318  ;  so  that  the  end,  or  foot,  may  give  a  line  of  a  slight 
variation  on  this  same  mean  value,  looking  to  the  expres- 
sion of  the  value  of  the  square  of  the  earth's  equatorial 
diameter  /;/  miles.  It  will  be  further  noticed  that  the  pyra- 
mid itself  is  a  change  on  the  standard  values,  so  that  its 

-  base  side  and  the  height  of  its  king's  chamber  shall 
4  &  o 

obtain  the  factor  6,  of  36  ;  and  so  likewise  here  after  the 
radical,  and  radical  use,  of  El,  or  31 ,  is  had,  it  is  made  her- 
maphrodite by  the  addition  of  the  letter  H,  or  5  ;  together 
framing  the  number  6  X  6  =  36.  So  these  two  numbers, 
31-1-5  =  36,  denote  the  pyramid  work  for  cosmical  meas- 
ures. 

Take,  now,  the  more  exact  enunciation  of  this  sentence  : 
B' — rash  is  213  —  2,  and  213  is  355  (one  of  the  pyramid 
forms  of   circumference    to    a    diameter  of   113)  X  6,  or 


1 82  Introduction  to  Appendices.  §  85. 


355x6  =  213-0;    where   also   355    is  the   Hebrew   word 
shanah  for  the  lunar  year.     But,  by  §  35  (3), 

(!•)     113     :     355-OOOI     '.'.     Z^    '-     113-098. 

Take,  therefore,  a  circumference  value  of  355.0001,  and 
cross  it  by  6  diameters  of  113. 100,  thus  subdividing  it  into  12 
compartments;  and,  by  means  of  the  form  of  36  :  113.098, 
as  denoting  a  straight  line  diameter  value  in  36,  the  whole 
value  can  be  changed  into  square  forms  of  6  X  6,  or  36  X  ^d' 
The  word  rash,  signifying  this,  the  letter  B,  ov  2,  shows 
that  this  form  is  to  be  used  twice,  either  together  or  sepa- 
rated. If  this  is  done,  then  113.098  becomes  226.2  ;  and, 
as  to  this,  see  the  measures  of  the  queen's  chamber,  §  79. 
Kabbalistically,  the  form  is  used  twice  as  signifying  the 
'■'measure  above''  and  the  '^  measure  below""  of  the  heavens 
and  of  the  earth ;  that  of  the  heavens  being  the  celestial 
circle  of  360°,  and  the  circle  of  the  same  value  served  to 
belt  the  earth. 

Now,  this  use  is  determined  by  the  use  of  the  full  word 
form  Elohimy  D*(l7K,  used  numerically,  and  in  a  determi- 
native form  of  what  is  being  done  in  a  general  way;  for, 
place  the  word  in  a  circle, 


and  then  reading  the  values  from  left  to  right,  we  have 
314^5'  or  the  relation  of  circumference  to  a  diameter  of 
one;  which  word,  as  a  whole,  then,  is  made  to  signify  the 
effect  of  the  detailed  values  of  the  radical  words  31,  and  5, 
or  El,  and  h.  This  enforces  the  parallelism  made.  But 
the  use  of  these  forms  in  the  pyramid  are  shown  to  develop 
the  measures  of  the  heavens  and  of  the  earth  ;  so  here,  for 
the  narrative  says,  that  in  them  (take  the  hithpacl  form 
of  the  verb)  developed  themselves  the    heavens   and  the 


§  85.  Introduction  to  Appendices.  183 


earth,  a  perfect  parallelism  in  one  way  and  use,  as  will  be 
seen,  of  the  same  forms.  Beyond  this,  taking  the  words 
'■''heavens''  and  earth:'"  heavens  is  shdmayim,  D^!Dt^,  and 
add  the  letter  signs,  we  have  3-J-4-I-1  +4=12.  Earth  is 
Arcts,  10i<,  and  add  the  letter  signs,  and  we  have  14-2  +  9 
=  12.  Then  each  of  these  words,  for  one  value,  sets  forth 
the  value  12.  Both  words  are  used  with  the  definite  ar- 
ticle n,  or  5,  and  this  can  be  used  either  as  5  or  .5  ;  so  that 
the  words  may  denote  the  use  of  12  with  the  factor  .5,  and 
12  X  -5  =6»  where  the  factor  6  is  again  indicated  as  twice 
used  to  form  a  line  of  12,  showing  use  of  the  same  factor 
value  as  to  the  heavens  and  the  earth,  with  a  fixed  rela- 
tion 12. 

Thus,  out  of  the  opposite  relations  of  diameter,  or  straight 
line,  to  circumlerence,  or  curved  line,  a  factor  value  is 
raised  to  apply  to  a  comparative  knowledge  of  the  heavens 
and  the  earth,  the  word  Elohim  determining  \h&  details  of 
work,  and  the  use  of  the  exact  circular  relation  ;  therefore, 
the  narrative  form  justifies  and  shadows  forth  the  exacter 
mathematical  and  astronomical  use. 

This  use  and  factor  form  underlies  all  that  follows.  Take 
tlie  unit  value  6,  as  connected  with  the  British  measures, 
§  30  («),  and  let  it  be  the  factor  number  of  the  hours  in  a 
day.  A  day  was  a  circle,  and  was  divided  into  day  or 
light,  and  evening  or  dark,  and  these  qualities  were  sexed, 
as  light  =^mah.,  and  nights  female.  By  the  Hebrew 
usage,  circles  were  displayed  as  squares,  and  a  day,  of  day 
and  night,  was  a  perfect  square  ;  but,  as  each  perfected 
work  had  of  itself  to  be  perfect,  and  the  day  was  male,  and 
the  mghtyemale,  here  was  (by  division  of  the  6  factor  cubes, 
or  squares,  into  two  parts  each)  an  oblong  for  each,  which 
would  not  do,  so  the  perfect  square  was  divided  into  4 
others,  which  were  perfect  in  themselves — i.  e.,  two  ferfeet 
males  and  two  perfect  females.  Now,  the  division  into 
smaller  circles  of  hours  carried  the  same  necessity  of  per- 
fection, and  therefore,  in  hours,  the  perfect  day  was  divided 
into  12  males  and  12  females.  (The  factor  square  di- 
vided =  2,  one  male,  one  female,  each  an  oblong ;  divided 


184  Introduction  to  Appendices.  §  85. 

again,  and  each  factor  sqnare  becomes  divided  into  /our 
parts,  each  a  perfect  square,  or  two  males,  two  females, 
or,  for  the  whole  6  factor  squares,  twelve  males,  twelve  fe- 
males.) Such  being  the  condition  of  preparation  after  6 
days  have  elapsed,  on  the  sixth  day  the  results  of  the  sixth 
day's  labor  culminating  in  the  fructifying  principles  of 
sacr,  membrutn  virile  and  nckahvcih,  yoni,  (see  Gen.  i.,  v. 
27),  are  commanded  to  multiply.  In  6  days  there  are  thus 
made  72  hours  of  night  and  72  hours  of  day,  and  72  X72 
=  5184,  or  that  subdivision  of  a  solar  day,  which,  with  144, 
constitutes  the  limits  of  the  British  long  measures, 

144  and  5184 ; 
and  these  limits  are  here  united  in  the  sixth  day,  for  now 
the  number  of  hours  are   144,  and  the  multiplication  or 
square  of  their  division  into  72   and  72  produces  the  other 
limit  5184.     Then,  as  above,  by  use  oi El^  or  31,  we  have 

144  —  31  =  113  5184  —  31  =  5153; 

thus  showing  that  the  sixth  day  introduces  us  to  the  use  of 
the  Parker  and  Metius  forms  of 

6561   :   20612  and  113  :  355, 
on  which  the   pyramid  relations  are  all  based.     And,  in 
fact,  this  does  introduce  to  the  seventh  or  circular  day. 

Arets,  earth;  Adam,  man;  and  h-adam-h,  earth;  are 
cognate  to  each  other,  have  a  like  signification,  and 
are  personified  under  one  form. 

(c.)  Now,  there  should  be  some  enunciation,  which 
WQuld,  in  a  generalized  or  narrative  descriptive  way,  rec- 
ognize this  numerical  or  measuring  use  as  connected  with 
the  phallic  ox  fructifying  form;  some  term  which,  by 
stated  qualities,  would  cosmically  embrace  all  under  these 
uses.  This  was  the  case,  and  the  showing  will  prepare  one 
to  enter  into  the  further  meaning  of  the  combination  of  the 
measuring  W\\h  iho.  phallic  scheme,  (i.)  An  earth  iovm. 
was  built  on  a  man  form  in  the  Bible,  for  the  word  Adam, 
for  man,  by  a  suffix  h,  became  Adani-h,  or  h-adam-h,  or 
the  fruitful  earth.  These  words  were  founded  on  the  rad- 
ical Dl,  dm  for  blood,  whence  Adam  (which  radical  un- 


§  85.  Introduction  to  Appendices.  185 

derlies  the  word  Dann\scus,  connected  with  Ellczcr^  or 
318,  the  steward  of  Abraham's  house).  Now,  from  D1, 
dm^  there  comes  the  form  Adaf/i,  Olii  ;  and  this,  as  a  verbal, 
has  the  meaning  /o  be  7-cd  or  blood-colored,  and  also  to 
bind,  to  jit  firmly  to  one  another.  The  Hifil  participle  is 
DnK"/t3,  or  Mddini,  and  this,  among  the  Hebrews,  was  the 
name  iov  Afars.  [See  Nork's  Worterbuch,  under  '■'■£^sau" 
and  in  other  places.  He  quotes  from  Jalkut  Rubeni.  The 
Rev.  Dr.  Julius  Goldammer  has  furnished,  also,  as  au- 
thorities for  this  :.  (I.)  Talmudic;  Pirke,  of  Rabbi  Eliezer, 
c.  18  ;  Midrash  on  Proverbs,  c.  9.  (2.)  Maimonides,  in 
his  "Moreh  Nebuchin."  (3.)  Solomon  Ibn  Gabriel,  in 
his  "Crown  of  the  Kingdom."  (4.)  77ie  Sohar.~\  Seyf- 
farth  Sciys  (Chronology,  page  33)  :  "In  what  language  did 
the  ancient  Egyptians  write?  This  was,  of  course,  the 
Coptic.  .  .  .  Now,  it  has  been  ascertained  that  the 
ancient  Coptic  was  far  more  nearly  related  to  the  ancient 
Hebrew,  or  Chaldee,  than  to  any  other  language  in  the 
world ;  that  a  great  many  grammatical  forms,  and  nearly 
all  the  Coptic  (Egyptian)  roots,  are  derived  from  the  ancient 
Chaldee,"  and  more  also  to  the  same  effect.  He  certainly 
establishes  this  by  the  constant  occurrences  of  examples. 

Now  the  Egyptain  god-name  for  Mars  was  Artes,  Jf}r/^^, 
Ertosi,  Eprcoac,  and  the  word  is  but  the  use  of  the  Chaldee, 
or  Hebrew  form  Arcts,  or  earth.  This  can  be  seen  at  once 
by  taking  the  consonants  of  the  word  and  dropping  the  ac- 
cessory vowels  :  thus  the  Egyptian  word  is  ARTS,  and  the 
Hebrew  word  is  ARTS  ;  and  just  as  in  the  case  of  Adam 
tor  man,  Mars,  and  earth,  here  there  is  Arets  for  earth  and 
Mars.  The  fact  seems  to  be  that  the  word  Mars  was  not 
so  much  a  person  as  a  generalized  term  for  the  cosmical 
phases  oi  production  and  destruction,  or  birth  and  death. 
Blood  was  life,  and  the  shedding  of  blood  was  as  much 
the  type  oi  conception  as  of  death,  or  slaughter.  And  so, 
in  fact,  did  the  Egyptians  esteem  this  god  as  the  Primal 
Generative  Principle,  combining  the  springing  of  all  things 
of  heaven,  of  earth,  and  of  humanity,  in  himself.  As  to 
this,  Seyffarth   (Beitraege  zur  kenntniss),  under  "/Ir/C5," 


i86  Introduction  to  Appendices.  §  85. 

Mars,  quoting,  says:  "  Addit  Cedrenus  (Salm.  i,C.): 
Stella  Martis  ab  ^gyptiis  vocatur  Ertosi  (plantare,  gene- 
rare).  Significat  autem  hoc  omnis  generis  procreationem 
et  vivificationem,  omnisque  substantias  et  materice  naturam 
et  vim  ordinantem  atque  procreantem."  So,  it  seems,  that 
his  being  the  god  of  war,  and  of  bloodshed,  was  but  a  sec- 
ondary idea  flowing  out  of  the  primary  one  of  shedding  of 
blood  in  conception,  for  the  first  time.  Thus,  the  words, 
are  the  same  for  ARTS,  Hebrew,  and  ARTS,  Egyptian, 
and  combine  the  primal  idea  of  earth  as  source;  precisely 
as  in  the  Hebrew  itself,  under  another  form,  Adam,  and 
Madim,  Jkfars,  are  the  same,  and  combine  the  idea  of  earth, 
with  Adam,  under  the  form  of  h-ad(ini-h. 

Now,  Mars  was  the  Lord  oi  birth,  and  oi  death,  oi gen- 
eration and  of  destruction,  oi  ploughing,  of  building,  of 
sculpture  or  stone-cutting,  of  Aj^ chit e dure,  of  the  origin 
of  measures,  and  of  their  uses;  in  fine,  of  all  comprised 
under  our  English  word  ARTS.  He  was  the  primal  prin- 
ciple, disintegrating  into  the  modification  of  two  opposites 
for  prodriction.  Astronomically,  too,  he  held  the  birth- 
place of  the  day  and  year,  the  place  of  its  increase  of 
strength,  Aries,  and  likewise  the  place  of  its  death, 
Scorpio.  He  held  the  house  of  Venus,  and  that  of  the 
scorpion.  He,  as  birth,  was  Good;  as  death,  was  Evil.  As 
good,  he  was  light;  as  bad,  he  was  night.  As  good,  he  was 
man;  as  bad,  he  was  woman.  He  held  the  cardinal 
points,  and  as  Cain,  or  Vulcan,  or  Pater  Sadie,  or  Mel- 
chizadek,  he  was  Lord  of  the  ecliptic,  or  balance,  or  line  of 
adjustment,  and  therefore  was  The  fust  One.  The  an- 
cients held  to  there  being  seven  planets,  or  great  gods, 
growing  out  of  eight,  and  Pater  Sadie,  the  fust  or  Eight 
One,  was  Lord  of  the  eighth,  which  was  Mater  Terra. 
The  pictured,  or  delineated,  symbols  of  his  power,  were  : 
Membrum  virile,  oi  '■'■  Martis  generatorisf  Testis  and 
Toni,  "  truly  the  female  pudenda  sacred  to  Mars,"  and 
equal  to  the  egg  with  the  central  germ,  or  the  circle  zuith 
the  central  point,  a  Pythagorean  emblem  ;  the  triangle; 
the  pcniapla,  or  the  outlined  form  of  the  pyramid  with  its 


§  85.  Introduction  to  Appendices.  187 

apex  and  base  corner-points  ;  the  Scala  for  measures  ;  also, 
the  rota,  or  crossed-wheel  or  circle  ;  and  many  others. 

Thus,  the  Mars  idea  is  a  generalized  one,  comprehend- 
ing, by  -pcrsonijicationy  all  the  properties  hereinbefore  com- 
bined ;  and  is  an  enunciation  which  will,  in  a  general  way, 
recognize  the  numerical,  or  measuring  system,  with  the 
■phallic,  as  combining  the  heavens  and  the  earth,  and  man 
and  woman.  This  is  a  brief  outline  of  the  volume  of  facts 
derived  from  historical  records,  from  hieroglyphic,  and 
Egyptian,  and  other,  sources,  to  be  found  in  the  work  of 
Professor  Seyffa-rth  ;  which  work  seems  to  be  of  great  value 
as  to  the  real  truths  regarding  these  matters. 

So,  Arcls,  earth,  and  Adam,  man,  and  Adam-h,  or  h- 
adam-h,  earth,  are  cognate  under  the  primal  form  oi source, 
in  Mars.  The  idea  was  to  commingle  and  commonize  all 
things,  whether  earth,  man,  woman,  time,  distance,  and 
solid  shapes,  under  a  one;  yet,  again,  to  separate  the  one 
into  a  working,  living,  fructifying  two. 

Enigmatical  Constructions  appearing  in  the  First  Face- 
Readings  of  the  Bible  Narratives. 

{d.)  Besides  the  class  of  readings  of  the  narratives  of 
the  Bible  mentioned,  there  are  still  others,  which,  while 
not  being  of  much  depth,  are  yet  removed  a  little  from  the 
first  face-reading,  and  require  for  non-orientalists  some  lit- 
tle instruction  to  realize.  These  serve  to  take  one  a  step 
further  in  the  development  of  the  first  face-reading.  In 
regard  to  the  Garden  of  Eden,  for  instance,  it  appears  on 
the  first  face  simply  as  a  locality  for  the  construction  of  the 
woman  ;  whereas,  by  an  orientalism,  it  appears  as  an  initi- 
ation of  the  knowledge  of  the  sexes.  The  allegorical  use 
or  purpose  of  the  Garden  of  Eden  description  of  the  dis- 
integration of  one  into  two,  in  its  descriptive  terms,  for  the 
elaboration  of  production,  is  very  happily  illustrated  in  a 
note  to  "  The  Story  of  the  City  of  Brass,"  in  Lane's  ele- 
gant translation  of  '-'■The  Thousand  and  one  Nights."  It 
is  as  follows  :  '*  A  certain  king  saw  a  beautiful  damsel  upon 
the  roof  of  her  house,  and  was  captivated  by  her  charms, 


i88  Introduction  to  Appendices.  §  85. 

and  learning  that  she  was  the  wife  of  his  Wezeer,  he  sent 
this  minister  to  examine  the  state  of  one  of  the  provinces, 
and  went  to  pay  her  a  visit.  But  he  received  from  her  a 
reproof  which  confounded  him.  He  quitted  her  abode 
abruptly,  leaving  his  seal  ring  by  mistake,  in  his  confu- 
sion, beneath  the  cushion  against  which  he  had  been  re- 
clining;  and  w^ien  the  Wezeer  returned  to  his  house,  he 
happened  to  put  his  hand  beneath  the  cushion,  and  there 
found  the  king's  seal :  so  he  separated  himself  from  his 
wife  for  the  space  of  a  whole  year,  not  even  speaking  to 
her.  She  knew  not  the  cause  of  his  anger  ;  and  at  length 
when  she  was  wearied  by  his  conduct,  she  complained  to 
her  father,  who  went  in  to  the  king,  and  finding  tlie  Wezeer 
in  his  presence,  and  the  Kadee  of  the  army  before  him, 
accused  the  Wezeer  in  these  words  :  '  May  God  (whose 
name  be  exalted)  amend  the  circumstances  of  the  king  !  I 
had  a  beautiful  garden,  which  I  planted  with  my  hand,  and 
I  expended  upon  it  my  wealth,  until  it  bore  fruit,  and  its 
fruit  was  ripe,  when  I  gave  it  to  this  thy  Wezeer,  and  he 
ate  of  it  what  was  pleasant  to  him,  after  which  he  aban- 
doned it ;  so  its  flowers  withered,  and  its  beauty  departed, 
and  its  state  altogether  changed.'  And  thereupon  the 
Wezeer  said,  '  O  king,  this  person  hath  spoken  truth  in 
that  which  he  hath  said.  I  guarded  it,  and  ate  of  it ;  but 
one  day  I  went  to  it,  and  saw  the  footstep  of  the  lion  there  ; 
so  I  was  afraid  of  him,  and  withdrew  myself  from  it.'  The 
king  therefore  understood  that  the  footstep  which  the  Wezeer 
had  found  was  the  king's  seal  that  he  had  left  by  mistake 
in  the  house  ;  and  upon  this  he  said  to  the  Wezeer  :  '  Re- 
turn, O  Wezeer,  to  thy  garden,  and  thou  wilt  be  safe  and 
secure ;  for  the  lion  drew  not  near  it.  It  hath  been  told 
me  that  the  lion  came  thither ;  but  he  did  it  no  injury,  by 
the  honor  of  my  fathers  and  my  ancestors ! '  So,  the 
Wezeer,  on  hearing  this,  said,  '  I  hear  and  obey.'  "  It  must 
be  remembered  that  the  mental  characteristics  of  the  ori- 
entals are  the  same  to-day,  as  they  were  when  the  descrip- 
tion of  the  Garden  of  Eden  was  drawn  ;  not  only  so,  but 
there  are  very  strong  evidences  that  "  The  Thousand  and 


§  85.  Introduction  to  Appendices.  189 

One  Nights"  are  of  enigmatical  construction,  containing 
even  the  same  pyramid  problems,  based  on  the  same  sys- 
tem, herein  set  forth:  this  being  the  method  of  its  hand- 
ing down.  The  author  has  never  examined  very  carefully 
into  this  matter;  but  refers,  as  instances,  to  "The  Story 
of  Noor-Ed-Deen  and  his  Son,"  and  to  that  of  "  Hasan-El- 
Basrah,"  in  Lane's  edition. 

For  the  purpose  of  merely  showing  an  allegorical  dis- 
play, barely  concealed  in  the  narrative,  take  the  following 
two    instances,    which    will     amply    suffice    the    purpose : 
(i.)  The  word  Samson  means  the  sun,  and  the  narrative 
is  a  history  of  his  travel  in  his  orbit.     Samson,  root  value 
C*^'C*  =  the  sun.     "  Tell  me,  I  pray  thee,  wherewith  thou 
mightest  be  bound  ?     And  he  said  unto  her.  If  thou  w^eavest 
the  seven  locks  of  my  head  with  the  web."     Again  :  "  If 
I  be  shaven,  then  my  strength  will  go  from  me. 
And  she  called  a  man,  and  she  caused  him  to  shave  off  the 
seven  locks  of  his  head  (i.  e.,  the  seven  months  of  the  fer- 
tilizing power  of  the  sun)  ;  and  his  strength  went  from  him. 
But  the  Philistines  took  him,  and  put  out  his  eyes,  and 
brought  him  down  to  Gaza  (or  Goat,  zodiac  sign  of  De- 
cember, or  winter  solstice),  and  bound  him  with  fetters  of 
brass  !  (the  change  of  color  from  the  golden  rays  of  sum- 
mer;)  and  he  did  grind  (or  continue  his  orbital  path)  in 
the  prison-house.     Howbeit  the  hair  of  his  head  began  to 
grow  again  after  he  was  shaven  (his  power  increased  after 
the  winter  solstice).     And  they  called  out  Samson  out  of 
the  prison-house,  and  he  made  them  sport ;  and  they  set  him 
between  the  pillars"     (2.)  Job  was  the  personification  of 
the  history  of  ihe  year.   The  prosperity  of  Job  was  checked  : 
(i)  at  the  time  of  plowing;   (2)  at  the  time  of  the  summer 
solstice ;   (3)  at  the  time  of  the  disposing  of  the  harvest ; 
(4)  at  the  time  of  the  vintage.    At  this  last  time  a  whirlwind 
came  from  the  desert,  and  blew  down  the  house.     (p5y  = 
Tsauphon  =  Typhon=T3'phoon  =  the  North,  the  ^-z^Z/side 
of  nature,  as  also  the  arid  heats.  Teman  was  bounded  north 
by  the  desert.     The    desert  was    significant  of  Typhon. 
Typhon,  the  brother  of  Osiris,  held  sway  beyond  the  gates 


ipo  Introduction  to  Appendices.  85 

of  Sheol,  and  was  also  represented  in  the  whirl-wind^ 
"Then  Job  arose, and  rent  his  mantle, and  shavcd\\\'&  head." 
(The  priests  of  Baal,  the  sun,  were  tonsured.) 
And  said.  Naked  came  I  out  of  my  mother's  womb,  and 
naked  shall  I  return  thither.  The  Lord  gave,  and  the 
Lord  hath  taken  away.  .  .  .  And  he  sat  down  among 
the  ashes."  (A  cloud  of  fresh  ashes  is  much  like  a  fall  of 
snow.)  "Now,  when  Job's  three  friends  heard  of  all  this 
evil  that  was  come  upon  him,  they  came  every  on^  from 
his  own  place. ''^  This  '-'•from  his  own  place  ^^  is  extremely 
significant,  and  is  explained  by  the  meanings  of  the  names 
of  his  three  friends  to  properly  carry  out  the  astronomical 
allegory.     Take  the  names  as  they  come  :  (i.)  Eliphaz  = 

riD-^7N=  God  of  Gold  =  Pluto ;  Temanite  =  [Dfl  =  ptD  = 
The  Concealed.  The  place  of  Pluto  was,  then,  the  five 
sections  under  the  royal  arch,  the  Pit,  the  Inferno,  of  which, 
as  an  Evil,  Typhon  held  the  gates  bordering  on  Libra. 

(2.)  Bildad  =  "nS"p  =  son  of  lateo  =  D"lS  =  Pluto ;  Shu- 
hite  =  mt^=  Grave,  or  cave,  or  dark  -place,  or,  again,  the 
Pit.  (3.)  Zophar  =  n5i;  =  Death;  Naamathite  =  HD^^J, 
of  whom  the  Rabbins  say  :  '•'•She  was  the  mother  of  the 
demons.'"  Thus  explains  itself  the  declining  of  Job  under 
the  portals  of  the  royal  arch  into  the_;ft^^  of  winter.  This 
expression,  "  to  his  own  place, ^^  is  also  made  use  of  as  to 
Judas  Iscariot  in  the  Acts.  Seyffarth  says  that  as  the  hie- 
roglyphs of  one  sentence  might  contain  the  necessary  con- 
sonants of  one  or  more  other  sentences,  to  avoid  confusion, 
the  special  use  was  settled  by  a  determinative  hieroglyph. 
So  with  Job.  To  fix  more  determinatively  the  recurrence 
of  the  seasons  by  law,  to  Job  was  at  the  last  given  three 
daughters  =  the  Three  Fates  (what  had  happened  to  him 
was  fated  by  the  necessities  of  the  seasons)  =  (i.)  Keren — 
happuch  =  Cornucopia  =  weaving  or  beginning  of  life. 
(2.)  Jemima  =  DV  =  day  =  ^w/arg-Zw^  the  days  of  life. 
(3.)  Kezia  =  ^^Vp=<:«//z«^==  the  cutting  the  threads  of 
life  :  and  this  betokened  that  the  same  history  was  con- 
tinually to  be  repeated. 

The   sameness  of  Arets,  earth,  and  Adam,  man,  and 


§  85.  Introduction  to  Appendices.  191 

h-adani'h^  the  earth,  and  the  Garden  of  Eden,  and  the 
womati,  and  the  seventh  day,  can  now  be  shown,  and  in 
such  a  manner  as  to  confirm  what  has  been  taken  above, 
as  the  numerical  system  of  the  Bible.  It  must  be  stated 
that  the  differing  meanings  based  on  the  hieroglyphic  idea 
are  so  conjluent  and  so  radiating  from  one  to  another 
subject,  3'et  all  united,  that  it  is  extremely  difficult  to  place 
the  results  of  deciphering  i^i  course;  and,  therefore,  a 
little  repetition  here  and  there  in  these  appendices,  and  a 
little  running  off  here  and  there  into  matters  not  specially 
germane  to  the  proper  subject-matter  in  hand,  at  any  place, 
must  plead  this  difficulty  as  an  excuse  and  an  apology. 


192 


Appendix  1.  §  86. 


APPENDIX  I. 

The   Ga7-dc)i  of  Eden. 

§  86.  The  earth  was  of  two  qualities,  one  named  sub- 
sequently to,  and  in  sequence  of,  the  other  ;  as  (i.)  Arcts, 
and  (2.)  Adain-h,  or  TP-Adam-h.  Commentators  have 
made  of  (i.)  the  dry,  arid,  tcnprodactivc  earth;  of  (2.) 
they  have  made  the  soil,  or  the  prepared  form  to  germi- 
nate. Proceeding  out  of  the  basic  numerical  values,  as  ab- 
stractions, it  has  been  seen  that  the  factor  value  6  has  been 
made  to  spring.  Take  the  word  JPArets  in  its  numerical 
use  of  12  X  -5  =6.  Here  the  factor  base  is  6,  while  the 
desired  number  is  the  aggregate  of  12,  of  which  there  is 
no  even  square  root.  It  is  given  as  an  abstract  quality,  in 
itself  an  idea,  and  in  itself  dry,  or  un/ruil/ul.  But  from 
the  transcendental  form  of  a  number,  as  of  a  line  having 
length,  but  without  breadth  or  thickness,  or  any  other  sub- 
stantive quality,  or  reality,  change  the  use  (preserving  the 
length  idea),  by  converting  it  into  the  area,  or  positive,  or 
real  form  ;  and  so,  12-  =  144,  or  the  square  of  12  equals 
an  area  of  144.  But  this  value  is  a  vjord,  and  the  word  is 
D"1J^,  or  Adam.  Supply  the  suffix  H,  or  h,  or  5  (which,  as 
the  half  of  one,  or  of  ten,  can  be  used  either  as  .5  or  5), 
or  the  female  quality,  making  the  word  hermaphrodite, 
and  there  results  n"Q1N,  or  144-5,  or  Adam-h,  v/hich  is 
the  word  earth,  alike  with  Arets,  earth;  and,  as  thus  seen, 
proceeds  from  its  use.  Proceed  as  if  the  form  meant  mul- 
tiplication, and  so  144  X  .5  =  72.  Taking  this  as  an  ab- 
stract number,  and  turning  it  into  an  area  form,  and  72^  ■= 
5184,  or  the  characteristic  value  of  one  solar  day.  But 
the  word  used  for  earth,  thus  derived,  is,  as  it  were,  the 
completed  form  JI- Adam-h, or  Adam, \\\\\i  a  prefixed  as  well 
as  suffixed  H,  or  h,  or  5.  Having  72,  as  Adam-h,  then 
for  H-Adam-h  there  is  72  X  5  or  by  .5,  and  this  equals 
360,  or  ■^G,  or  the  great  measuring,  astronomical,  and  geo- 


§  S6.  Appendix  I.  193 


graphical  circle.  So,  Arcls,  ov  6-|-6  =  i2,  the  abstract 
form,  becomes  Adaiu-h,  or  144-5,  and  h-Adam-h,  5-144-5, 
another  or  squared  form  of  itself,  with  the  factor  value  5  at- 
tached. Now,  it  is  said  that  Elohim  took  Adam,  or  man,  as  a 
fractional  portion,  from  h-Adam-h,  the  earth;  or,  he  took 
him  as  144  from  5-144-5 — that  is,  Adam,  man,  or  144,  is  thus 
derived,  and  is  the  square  of  6  +  6  =  12,  or  is  a  square  of 
foursquares  of6x6==36  each;  and  36x4  =  144,  and 
144  X  -5  =  72  ;  and  72  is  the  square  root  of  one  solar 
day  value;  which  144  is  the  area  value  of  the  British  foot 
in  square  inches.  Here  Arcts,  earth.  Mars,  becomes 
Adam-h,  earth.  Mars,  and  also  Adam,  man.  Mars;  while 
the  paralleled  mathematical  use  is  seen  to  event.  It  may 
be  observed  that  the  word  "l£3^,  ofhr,  for  "■dust,'"  is  rather 
broken,  ox  fractional  farts,  the  idea  of  dust  being  second- 
ary, as  a  comminuted  condition  of  parts  of  the  earth. 

Take  the  word  j"T^"p,  Gan-Odcn,  or  Garden  Bden,  and 
add  the  letter  signs  as  they  run,  or  3  +  5  +  7+4-1-5  =  24; 
the  numerical  value  is  24,  and,  to  show  the  factor  6,  this 
becomes  24  -r-  4  =  6,  or  the  24  indicates  four  parts,  of  6 
each.  Cross  12,  or  a  line  of  12,  on  itself,  and  there  results 
the  sign  of  the  letter  il,  or  tau,  whose  sign  value  is  4,  and 
w^hose  symbol /5 +.  Complete  the  square  on  each  factor 
of  '6,  and  there  results  the  completed  square  of  12  X  12  = 
144,  composed  of  four  small  squares  of  6  X  6,  or  ^6  each. 
This  is  the  nucleus  form  of  the  garden.  In  this  garden, 
the  Lord  God — that  is,  Jehovah  Elohim — placed  the  man, 
as  Adam.  As  Ada?n,  he  -was  144,  and  thus  he  is  himself 
the  nucleus  of  the  garden.  Up  to  this  Biblical  phase,  the 
god-name  has  been  Elohim,  among  whose  indications  was  '' 
that  of  circumference  to  a  diameter  of  ^«<?,  or  31415.  Now, 
the  other  god-name  is  brought  tbrward,  or  mH*,  or  yeho- 
vah.  For  one  use,  this  is  to  indicate  a  diameter  value, 
either  as  a  straight-line  one  of  a  denomination  of  20612,  as 
has  been  shown,  or  else  as  follows  :  The  running  values 
of  the  word  are  565  ^ ,  as  the  letters  read.  It  has  been  seen 
in  Adam-h  how  suffix  or  prefix  may  be  used  as  the  factor 


194 


Appendix  I. 


§86. 


5,  or  .5.  So  here  the  use  of  *  may  be  similar.  Take  the 
form  113  :  355,  where  113  is  the  diameter  value.  113  X. 5^ 
56.5.  The  letter  values  for  this  are  Hin,  or  Eve^  or 
womatiy  and,  as  a  word,  this  is  the  half  of  this  word 
niiT .  *  =  I  or  10.  Then  56.5  X  »  %  or  the  full  letter  form 
r\T\y',  equals  113  X  5  =  565.  Thus  it  is  seen  that  this  word 
is  from  the  value  113,  a  diameter  value.  The  use  of  the 
two  words,  Jehovah  Elohim,  or  Lord  God,  then  denotes  this 
character  or  condition  of  values  of  shapes  in  this  Garden 
of  Eden  production.  In  §  35  (3.)  is  to  be  found  the  form — 
(i.)     6561  :    20612     ::     1.90985  :  6 

(2.)        113  :    355.0001     ::     6  X  6  =  36  :    113.098+, 
where  these  circular  values  are  made  to  produce,  and  in- 
volve themselves  with  the  factor  6. 


& 

ss 

6 

Take  the  form  of  the  nucleus  of  the  garden,  or  four 
squares  of  6  X  6  =  36  each  ;  all  equal  to  one  square  of 
12  X  12  =  144.  Change  36  from  area  into  line  value, 
then  the  cross  -\-  becomes  extended  so  that  the  four  arms 
are  each  36  in  length,  or  as  to  each  arm,  have  now  be- 
come equal  to  the  third  term  of  (2.),  for  a  diameter  value 
to  a  circumference  of  113.098  (or  a  circumference  value  to 
the  king's  chamber  height  number  of  1.9085  x  6)*  Complete 
the  large  square;  and  now,  Adam,  or  144,  being  the  nu- 
cleus, the  garden  has  enlarged  to  four  squares  of  36  x  3^ 
each,  or  1296  in  area  each,  the  numerical  value  of  the 
square  yard  British  ;  or,  again,  each  one  is  now  Jared,  or 
IT,  or  Yard,  the  source  of  descent  (§33,  (6.)  note).    The 


§  87.  Appendix  I.  195 

aiTgregate  of  the  four  squares  is  1296  X  4  =  5184  ;  or  the 
Garden  of  Eden  is  now  become  a  unit  measure  of  time^ 
based  on  the  value  of  the  solar  day,  raised  from  \}a^  factor 
6,  through  the  terms  of  land  measure — viz.,  the  inch, 
ihe/bot,  and  the  yard;  and,  as  to  this  last,  it  has  been  seen 
that  it  indicates  the  other  limit  of  the  British  measures — 
viz.,  that  of  the  acrr,  and  that  of  the  mile  value.  (§  §  58,59.) 
This  being  the  framework,  and  these  being  the  different 
kinds  and  qualities  of  measures  involved,  proof  can  now 
be  made  that  all  that  has  been  said  has  been  well  taken  as 
the  Biblical  intent.  Our  cross  line  has  now  become  36  and 
36,  together  equal  to  a  length  of  72  ;  but  ^6  comes  under 
the  form  113.098+  circumference  :  36  diameter,  which 
form  was  derived  from  another,  as  follows  : 

(3.)     113.098+    :    36    ::    355-OOOI    '■     "S- 
There  is  now  to  be  exhibited  the  collateral  use  of  the  last 
part  of  this  form — viz.,  of  355.0001   :    113. 

The  Production  of  the  Woma?i  from  the  Man, 

§  87.  Eve  was  the  wife  of  Adam,  and  she  was  taken 
out  of  his  side.  And  H^Ada^n,  DlNTT,  the  man,  said  : 
"She  shall  be  called  wojuan,  because  she  was  taken  out 
of  man  (or  aish,  or  CJ<) ;"  where,  for  the  matt  out  of  whom 
woman  was  taken,  the  word  now  becomes  changed  from 
Adam  to  Aish,  from  DIN  to  C^'N.  And  this  is  the  basic 
determinative  of  the  process  of  construction  of  the  woman  ; 
for  aish,  or  J^^N,  is,  adding  the  letters  311,  or  reading  them 
as  the  word  runs,  and  the  numerical  value  is  113  ;  which, 
underthis  word  fl;/^/^,  gives  for  use  the  form  of  113  :  355.0001, 
connected,  as  seen,  with  the  other  form  of  113.098  :  1,6; 
which  last  form,  in  the  value  36,  eventuated  above,  from 
the  placing  of  Adam  in  the  garden.  So,  from  Adam,  man, 
144,  comes  aish,  man,  113. 

(a.)  It  is  observed  that  this  113  is  a  straight  line,  or  di- 
ameter value,  and,  as  the  cross  line,  which  is  36  and  2^, 
indicates  113.098  for  each  ;^6,  we  can  take  the  113.098  for, 
or  as,  the  equivalent  expression  of  36  ;  and  then  the  varia- 
tion of  113  for  113.098;  both  belonging  to  the  same  form. 


196 


Appendix  I. 


§87. 


Then  we  have  for  36  and  2^,  113  and  113.  Now,  this  is 
an  abstract,  or  mere  length  relation.  Convert  it  into  an 
area  value,  either  by  raising  a  square  on  the  line  113,  or 
else  by  taking  the  square  root  of  this  value.  Take  the 
latter  plan,  and  so — 

(!•)  7113^10630+, 
as  the  value  of  the  side  of  the  man,  or  of  the  square,  thus 
reduced,  far  enough  for  the  purposes  intended.  Divide  this 
resulting  square  into  four  others,  thus  producing  the  crossed 
condition  of  the  interior,  making  the  figure  similar  to  the 
Adam  form  above  ;  then,  each  side  of  this  square,  of  the 
value  of  10630,  will  be  divided  into  two  values,  each  of 
which  will  be — 

(2.)      10630-^2  =  5315; 
and  this  is  the  sought  for  result  that  shows  that  this  was 
the  process  of  obtainment.     For,  place  the  Hebrew  letters 
lo  this  result,  as — 

(3.)   n  V  N  n 
5315 

and  this  word  thus  framed,  in  Hebrew,  is  by  translation — 
(4.)      The  zvoman. 
(d.)     In  form,  the  geometrical  figure  now  conforms  with 
the  others  made  of  the  garden,  thus — 

J  o  c  a  o 


SOI^ 

S  13  S 

the  interior  cross  lines,  showing  the  division  made,  the 
horizontal  cross  line  cutting  this  reduced  form  of  man,  or 
113,  in  his  side.  The  side  thus  shown  is  the  middle  of  his 
height.  Now,  after  having  the  grand  determinative  of  the 
basic  value  113  given,  as  that  the  ivoman  was  to  be  taken 


§87. 


Appendix  I. 


197 


out  of  ais/i,  vian,  or  113,  this  determinative  is  accompanied 
by  a  natural  one,  running  with  the  narrative.  113  :  355 
is  a  circular  form  denoting  diameter  to  circumference.  The 
reduced  form  of  ^nan  shows  that  the  woman  value  is  but 
a  reduction  from  this  original  form,  and,  as  shown,  it  is  the 
Aa/y  cross  line  of  the  square,  indicating  a  radius,  or  half 
diameter  value.  Under  the  form,  this  would  correlatively 
indicate  a  se7ni-circumfcrencc.  Now,  the  narrative  reads 
that  the  woman  was  taken  not  only  out  of  the  side  of  the 
man,  as  shown,  but  also  that  she  was  thus  taken  as  a  rib. 
And  this  is  the  determinative,  for  the  rib  of  a  man  extend- 
ing from  the  backbone  around  to  mid-front,  is  a  senii- 
circumfercnce. 

The    Woman  Form    of  the   Garden,  the   Source   of  the 
'■'Holy  of  Holies,"  and  of  the  Four  Typical  Rivers. 

{ci)     (i.)  Draw    a  square,  crossed  interiorly,  to   exhibit 
to  the  eye  what  has  been   done,  and  on   the   cross   lines, 
place  the  numerical  values  of  the  results  (i.  e.,  the  woman 
or  5315)'  thus— 


/ 

s\      ms 

53\.       \S 

9 

i 

The  woman,  or  the  definite  article  the,  or  ,1>  and  woynan, 
or  Ash-h,  or  HCK,  is  produced  from  man,  113.  Separate 
the  definite  article,  or  H,  or  5,  from  the  remaining  figures 
of  the  word,  into  the  central  square  shown,  now  triangu- 
lated with  respect  to  the  large  one.  There  results  two 
cross  lines  of  5  -|-  5  each  (or,  if  the  central  figure  be  made 
to  assume  the  form  of  a  square,  on  these  lines,  there  re- 
sults a  square  of  5  -|-  5  =^  10  to  the  side),  as  to   its   dimen- 


198  Appendix  I.  §  87. 

sions.  But  the  number  10  is  the  perfect  one,  and  a  'Je- 
hovah value  (§  82),  and  by  Hebrew  Kabbalah,  the  letter 
n,  or  number  5,  is  the  womb.  "  The  Rabbins  have  a  say- 
ing that  God  made  all  things  out  of  the  letter  ,1."  (Sod. 
Genesis,  p.  196.)  "  Jl  and  ^  wedded  (that  is,  il,wo/nd,  and 
»,  mcmbrimi  virile'),  begot  the  1,  or  letter  z'^z/,  which  stands 
as  the  center  pillar  of  the  visible."  (Dr.  Goldammer,  as 
from  Sohar  [The  World].)  Thus,  also,  the  number  10,  or 
letter  *,  as  of  10  cubits,  is  the  value  of  the  holy  of  holies 
in  the  temple,  as  to  its  most  sacred  precincts,  between  the 
cherubims.  Here  this  holy  of  holies,  this  10  combining  in 
its  pictured  form  both  phallus  and  yoni,  is  the  perfect  one 
cube  com.posed  of  eight  othersof  the  valueof  5,  or  T\,  each, 
the  total  forming  the  male-female  in  one,  10,  as  here  the 
■womb  of  the  Garden  of  Eden,  or  Paradise.  Plainly,  the 
woman  part  of  woman  is  the  womb ;  all  the  rest  is  con- 
nected with  its  egress-way  to  the  light:  therefore,  \\-\Q.four 
ways  marked  from  the  center,  are  the  four  great  rivers^ 
as  denoted  in  the  narrative.  In  the  narrative,  these  rivers 
are  designated  as  flowing  from  the  garden,  and  are  taken 
as  having  their  rise  in  its  midst. 

(2.)  But,  as  one  kind  of  symbolization  but  leads  to  an- 
other, and  as  the  mathematical  and  geometrical  system  is 
the  essential  one,  these  arrangements,  while  perfectly  con- 
forming to  one  or  more  other  kinds  of  conditions,  should 
become  subservient  to  the  more  essential  uses  ;  and  such  is 
the  case.  Having  dropped  the  prefixed  letters,  or  num- 
bers, in  the  center,  where  they  especially  belong,  make  use 
of  those  left,  in  the  order  found,  by  placing  them  in  a  cir- 
cle, thus  : 


And  here,  by  reading  the  values,  one  finds  the  form 

113   :    355 


§  37.  Appendix  I.  199 

ready  made  to  his  hand.     Compress  the  values  to  read  two 
and  two,  from  right  to  left,  and  the  form  of 

5         5         3 

311 
results  ;  where,  in  addition  to  the  above,  we  have  the  great 
differential  value  31,  connecting  the  extremes  144  and  5184 
of  the  British  measures,  as  /ow^.and  time  measures,  with 
the  forms  113  :  355,  and  5153  X  4  =  20612  :  6561  (§  35 
(3.)  (4.),  actually  accompanying  the  forms  it  thus  gives  rise 
to ;  for,  while  the  form  is  113  to  355,  after  reading  the  dif- 
ferential 31,  there  follows  the  reading  5153,  the  Parker 
area  of  the  circle  inscribed  in  the  square  of  6561,  and  the 
base  of  the  form  20612  :  6561.  Thus  this  form  of  the 
crossed  garden  raises  those  forms  of  original  measure, 
which  are  emblematically  displayed  by  a  mayi  fastened  or 
nailed  to  a  cross.     §  21. 

Other  Dcteryninatives. 

(d.)     Besides  the  determinatives  given,  there  are  others, 

here  and  there  in  the  narrative,  pointing  and  determining 

the  process  of  elaboration  of  the  numerical  and  geometrical 

forms,  as    being   correctly  taken.     Some    can    be    given. 

(i.)  When  Adam  is  placed  in  the  garden,  preparatory  to 

the  woman  being  taken  from  his  side,  it  is  said :  "And  the 

Lord  God  caused  a  deep  sleep  to  fall  upon  //'Adaju,  and 

he  slepty     The  verbal  and  he  slept  is  the  determinative  of 

the  process.     The  word  is  |tr*^"),  vyishan,  and,  supplying 

the  values,  they  run  61 135.     Supply  a  cipher  for  the  10 

in  ♦,  and  we  have  601 135,  which,  bent  into  the  circular 

form,  runs,  or  reads,   106135,  where  106  is  the  running 

determinative   of  the  J  of  113,  the  first  three  figures  of 

which  are  106,  and  the  remaining  figures,  or  135,  are  the 

result  to  be  derived,  or  woman,  or  nt^J<=i35.     (2.)  At 

the  close  of  the  process  there  is  the  following  statement  : 

"And  he  brought  her  unto  the  Adam.'"     This  is  a  double 

determinative,  connecting  the  woman,  who  has  been  taken 

from  aish,  man,  with  the  other  form  of  man — viz.,  Adam. 

The  Hebrew  words  are  Dli^H/J^n,  Ha  El  Ha  Adam,  and 


200  Appendix  I.  §  88. 

the  running  values  are  5135  —  144,  or  the  -woman  with 
Adain,\\'\G.  otherformof  ?;^««.  (3.)  Besides  other  things,  there 
is  reference  to  a  small  square  in  the  center,  on  the  crossed 
lines,  giving  rise  to  further  reference  values.  The  smallest 
squared  division  of  the  square  of  144  is  the  small  square  of 
3X3=9-  Four  of  these  on  the  crossed  lines  in  the  center 
of  the  Adam  square  give  a  unit  square  of  6  X  6==  2)^,  as  a 
total.  There  are  then  4  squares  of  the  square  of  3,  where 
the  factors  3  and  4  are  designated,  or,  together,  the  equiv- 
alent of  the  golden  candlestick  arrangement  of  3  +  4  =  7. 
But  each  small  square  is  of  3  X  3  ==  9.  Then  the  numbers 
7  and  9  are  used,  or  can  be  used,  in  relation  to  this  smaller 
square.  It  is  observable  that  this  small  square  is  the  one, 
then,  at  the  center  of  the  Adam  square,  or  at  the  cleft  or 
division  lines  of  the  garden.  The  Hebrew  values  for  7 
and  9  are  characteristic  of  the  letters  ^  and  V-  Put  them 
together,  and  there  results  Vj7,  or  ots,  or  the  word  for  tlie 
tree  in  the  garden.  But,  as  by  the  division,  it  is  two  trees 
twisted  or  bound  in  one,  then  7  x  9  =  63,  which,  read  in 
the  reverse,  is  36,  or  the  value  in  area  of  this  small  square, 
or  the  unit  factors  6  X  6  =  36  ;  and  this,  reading  in  the  re- 
verse, is  rulable  by  Kabbala. 

(e.)  In  the  forms  (i.)  113  :  355  and  (2.)  36  :  113.098, 
while  the  first,  or  (i.),  is  used  as  the  abstract  form,  there  is 
an  indication  that,  under  the  form  of  aish^  C**N  =  113,  the 
circumference  value  of  113.098  is  implied  ;  also,  the  113  in 
(i.),  as  seen,  is  a  diameter  value.  The  indication  of  the 
second  use  is  thought  to  be  in  the  word  anashiin,  D^uOi^, 
men,  plural  of  ^*'K,  man ;  for,  bend  this  into  a  circle,  and 
we  find  a  reading  of  the  continuous  numbers  31415,  or  of 
circumference  to  a  diameter  of  one. 


The   Garden  of  Eden  as  the  Seventh  Day. 

§  88.  It  will  be  shown  how  355,  as  the  circle  of  113,  was 
used  for  the  purpose  of  correlating  natural  periods  of  time 
with  this  abstract  circular  value.  It  has  been  seen  how 
this  form,  with  that  of  Mr.  Parker,  is  connected  with  square 


§  88.  Appendix  I.  201 

measure  in  the  use  of  the  factor  6.  It  has  just  been  shown 
how  the  Garden  of  Eden  assumes  the  function  of  assimilat- 
ing both  methods.  Now,  with  the  6  days  closed  the  square 
measure  form,  and  with  the  7th,  came  its  application  to  the 
circular  relation.  This  7th  day  was  the  day  set  apart  as 
the  woman  or  circular  day.  Just  as  it  has  been  seen  that 
the  holy  of  holies  and  the  sacred  10  are  designated  sex- 
ually as  connected  with  the  substance  of  the  garden,  as 
being  the  womb,  or  productive  element,  so  the  7th  day,  in 
its  turn,  is  but  a  correlated  form  of  this  same  garden,  in  the 
form  of  a  circular  day.  The  sameness  is  observable  in 
one  respect,  for  it  is  seen  that  the  numerical  value  of  the 
largest  extension  of  the  garden  is  the  value  of  four  square 
yards,  or  1296  ><  4  =  5184,  or  the  characteristic  value  of 
one  solar  day.  Then  the  7th  day  /s  the  Garden  of  Eden, 
and  is  allied  in  holiness  with  the  holy  of  holies  and  the 
perfect  value  10.  Of  this  day  it  is  said  that  Elohim  (31415) 
blessed  and  sanetified  it.  Just  as  the  word  zacr,  or  sacr, 
the  special  word  for  incinbrum  virile,  is  translated  by  the 
generalized  term  male,  just  so  the  word  sanctijicd  is,  by 
translation,  wrested  from  its  proper  specialized  meaning, 
as  having  relation  to  this  day.  The  sacr  was  that  with 
which  the  Lord  should  be  memorialized.  The  custom  was 
to  make  memorial  before  the  Lord  with  the  sacr.  The 
word  being  retained,  but  losing  its  primitive  use  and  force, 
became  the  Latin  sacr^/actuvi,  then  saerifacio,  then  the 
English  sacrifice;  and  is  at  the  foundation  of  the  word 
sacrament.  The  signification  is  obvious  :  Just  as  the  sacr 
denoted  the  means  of  germination  of  a  nezu  existence,  so 
its  use,  as  related  to  man's  connection  with  another  realm  of 
life,  shadowed  forth,  in  whatever  other  use  was  being  made, 
as  of  bread  and  wine,  that  in  these  means  resided  the  germ 
of  that  existence,  and  that,  like  the  sacr,  these  (bread  and 
wine)  were  the  vehicles  of  its  planting.  The  word  sanc- 
tified is  kodcsk,  t^np,  and  this  was  a  word  for  prostitution, 
for  holy  purposes,  at  the  temples — esteemed  to  be  a  pure  and 
sacred  use.  Kodesh,  uHp,  to  he  fresh,  nezu,  -pure,  shin- 
ing, is  the  same  with  kodesh,  or  chodesh,  i^^pf  ^'^  he  fresh, 


202  Appendix  I.  §  88. 

^ure,  new,  young;  which  last  word,  as  substantive,  has 
the  meaning  of  the  time  of  the  new  moon,  which  period  of 
lime  in  nature  regulated  or  marked  the  recurrence  of  the 
menstrual  flow,  as  7  X  4=  28  days.  The  character  of  the 
meaning  exactly  fits  to  the  meaning  of  the  word  as  applied 
to  the  7th  day.  Here  it  has  reference  to  the  quality  of  the 
7th  day.  The  word  blessed  is  the  verbal  b'arak,  or  *]*1D, 
and  giving  its  values  is  222.  While  this  is  the  same  value 
with  ^"1^,  cherub,  which  is  taken  to  signify  the  cubit  half 
base  side  of  the  pyramid  structure  [§  84  (3.)],  and  which 
measure  is  specified  in  the  narrative  description  of  this  gar- 
den, it  is  thought  here  to  have  reference  to  a  like  relation 
to  the  number  7,  as  this  7th  day,  for  2.22-[-  is  the  diameter 
to  the  number  7  taken  as  a  circumference.  Now,  it  has 
been  seen  that  the  idea  of  the  garden  was  that  it  should  be 
a  source  of  birth  of  time,  and  oi  distance  measures,  under 
a  womb  use.  It  was  a  part  of  the  cosmogony,  that  all 
things  arose  from  a  common  unit  source,  to  which,  by  links, 
they  could  be  made  to  refer  co-ordinately.  Having  thus 
symbolized  the  use,  how  was  it  to  be  made  good?  Here, 
again,  comes  corroboration  of  the  system  ;  for  it  was  only 
through  the  woman  that  the  proper  relation  could  be  ar- 
rived at  and  shown.  As  the  factor  6  lay  at  the  foundation 
of  other  kinds  of  measure,  so  did  the  number  7  for  this 
especial  use:  for  7X4=^28  days,  a  menstrual  period; 
28  X  10  =  280  days,  a  period  of  gestation,  and  28  X  13  = 
364  days,  a  luni-solar,  or  week,  year,  as  52x7^364' 
And  this  was  the  numerical  factor,  which,  as  applying  to 
human  birth,  would  practically  co-ordinate  human  birth 
with  the  other  system  of  measures  set  forth  in  this  garden. 
Such  being  the  use  of  the  7th  day — viz.,  harmonizing  it 
to  show  forth  this  especial  use — there  is  very  much  to  con- 
firm what  has  been  said  regarding  this  use.  In  the  second 
volume  of  Sharpe's  history  of  Egypt,  page  202,  he  says : 

"  The  Eleusinian  mysteries,  withhi  the  temple  of  Ceres  (bread) 
and  Proserpine  (gate  of  Scorpio,  autumn,  and  wine),  in  the  south- 
east quarter  of  Alexandria,  which  had  been  brought  into  the  city 
in  the  reign  of  Philadelphus,  had  now  lost  their  sacredness,  and 


§  88.  Appendix  I.  203 

very  much  of  their  secrecy.  The  priestesses  had,  for  four  cen- 
turies, walked  in  procession  through  the  streets,  carrying  a  sacred 
basket;  and,  latterly,  it  had  become  known  that  this  basket  held 
a  live  serpent^  supposed  to  be  the  author  of  sin  and  death." 

He  quotes  from  Eusehius  fracp.  Evang.^  Lib.  III.  12. 
He  also  copies  from  a  coin  in  the  Pembroke  collection, 
which  represents  a  basket  with  raised  lid  and  a  serpent  is- 
suing forth.  The  basket  is  surrounded  b}'  a  wreath  of 
Jlowcrs  and  frtiit,  but  the  flowers  are  of  a  kind  that  bloom 
but  once  a  month,  and  the  fruit  is  the  basket  or  scrotum 
representation. 

"  The  mystic  basket"  of  the  mysteries  contained,  among  other 
things,  "  thejigure  of  a  serpentP  (De  Sacy,  318,  319.)  "Also, 
in  the  most  ancient  mysteries  of  the  Greeks,  they  shouted  Eva! 
and  at  the  same  time  a  serpent  was  shown.  (Orelli,  Sanchon, 
pp.  14,  45.)  "  The  Bacchi  celebrate  the  mysteries  crowned  with 
the  serpents^  shouting  aloud  Evaf'  "  The  name  Hevia  (Evia) 
roughened,  is  interpreted  ihe  female  serpent" — that  is,,  chouva, 
TDT]^  ^ov  T\')'n,  Eva.  (Clemens  Al.  Cohort,  ad  Gentes,  it,  12.) 
(Qiioted  from  Sod.  pp.  105,  106.)  "  The  cry  made  by  the  females 
in  their  lamentations  in  these  mysteries  was  Eva!' "  (Land- 
marks Freemasonry,  Vol.  II.,  p.  4S0,  note.) 

The  letter  0  is  the  symbol,  at  the  same  time,  of  a  serpent 
and  a  basket.  It  is  3  X  3  =9,  and  is  at  the  center  of  the 
garden.  The  name  of  David  was  basket.,  "  prop,  a  thing 
woven,  for  figs."  A  very  slight  change  from  this  v/ord 
DUD,  or  DUDI,  is  the  same  in  meaning  as  basket.,  but  in 
the  plural  is  '•''love-apples,^^  etc.  (Song  of  Solomon,  vii.  14.) 
Thus  the  scrotum  is  signified  with  the  male-female  combi- 
nation, which  was  sin,  and  by  a  figure  was  birth  under  a 
form  of  death;  just  as  it  is  a  fact  that  the,  to  some  lugu- 
brious, S3'mbol  of  scull  and  crossed  bones,  as  signifying 
death,  to  bthers  is  the  most  precious  emblem  of  life.  See 
also  Dr.  Inman's  pictured  descriptions  of  the  asheras  or 
groves.  A  vertical  narrow  door,  closed  with  thongs,  sur- 
mounted by  a  radiating  fan-shaped  ornament  of  7  rays,  sur- 
rounded by  bunches  of  flowers,  the  number  of  the  bunches 
being  6+7  =  13.     This  is  a   symbol  of  the  Garden  of 


204  Appendix  I.  §  88. 

Eden.     The  Hindu  representation  of  the  garden  is  still 
plainer. 

Note. — The  mystery  of  the  cross  deepens,  rather  than 
clears,  as  uses  of  it  are  found  here  in  the  substance  of  this 
garden,  and  also  primordially.     The  Hebrews  have  handed 
down  by  targuins,  readings  which  have  been  obscured  by 
translation.     Joshua  viii.  29,  they  read  in  the  Arabic,  and 
in  the  tar  gum  of  'Jonathan,  "  The  king  of  Ai  he  crucified 
upon  a  tree."     The  Septuaginta  rendering  is  of  suspension 
from  a  double  -wood  or  cross.     (Wordsworth  on  Joshua.) 
The  word  is  (l/D,  Tdlah,  and  may  derive  the  cross  idea 
from  the  fl,  or  +.     The    strangest  expression  of  this  kind 
is  in  Numbers  xxv.  4,  where,  by  Onkelos  (?),  it  is  read, 
'■'■Crucify  them  before  the  Lord  {fchovah)  against  the  stm." 
The  word  here  is  j^p\  to  nail  to,  rendered  properly  (Fuerst) 
by  the  Vulgate,  to  crucify.     The  very  construction  of  this 
sentence  is  mystic.     The  symbolization  of  the  connection 
of  113  :  355,  with  20612  :  6^61,  hy  3.  crucified  man,  \s  vlv.- 
mistakable,  and  here  it  is  found  as  essential  in  the  structure 
of  the  Garden  of  Paradise.     The  theoretical  use  of  cruci- 
fixion, then,  must  have  been  somehow  connected  with  the 
personification  of  this  symbol.     But  how?     And  as  show- 
ing what?     The  symbol  was  of  the  origin  of  measures, 
shadowing  forth  creative  law  or  design.    What,  practically, 
as  regards   humanity,   could    actual   crucifixion   betoken? 
Yet  that  it  was  held  as  the  efligy  of  some  mysterious  work- 
ing of  the  same  system,  is  shown  from  the  very  fact  of  the 
use.     There  seems  to  be  deep  below  deep  as  to  the  myste- 
rious workings  of  these  number  values.     Not  only  are  they 
shown  to  work  in  the  cosmos,  but  also  they  are  made  use 
of  by  Daniel,  the  -prof  hct,  as  the  guide  to  his  prophetic  ut- 
terance.    By  sympathy,  they  seem  to  work  out  conditions 
relating  to  an  unseen  and  spiritual  world,  and  the  prophets 
seem  to  have   held  knowledge  of   the  connecting  links. 
Reflection  becomes   more    involved  when  it  is  considered 
that  the  power  of  expression  of  the  law,  exactly,  by  num- 
bers clearly  defining  a  system,  was  not  the  accident  of  the 


§  88.  Appendix  I.  205 

language,  but  was  its  very  essence,  and  of  its  primary  or- 
ganic construction  ;  therefore,  neither  the  language,  nor  the 
mathematical  system  attaching  to  it,  could  be  of  man's  in- 
vention, unless  both  wertijvunded  upon  a  -prior  language, 
-which  afterward  became  obsolete.  For  instance,  the  word 
aish,  C***^,  man,  is  probably  the  ^/'/;;/(9r^/rt/ word — the  very 
first  word  possessed  by  the  Hebrews,  whoever  they  were, 
to  carry  the  idea,  by  sound,  of  a  man.  The  essential  of 
this  word  was  113  from  tlie  beginning,  and  carried  with  it 
the  elements  of  the  cosmical  system  displayed.  Whence 
then  the  language,  and  its  power  as  the  vehicle  of  a  natural 
cosmical  system,  tml ess  from  an  unseen  spiritual  source? 
And  if  this  is  so,  all  that  pertains  to  the  showing  forth  the 
conditions  of  the  working  of  this  law,  as  by  these  symbols, 
and  their  real  personification,  would  seem  to  have  determi- 
nation in  the  same  spiritual  realm. 


2o6  Appendix  II.  §  89. 


APPENDIX   II. 

Time  Calculations  founded  on  Abram,  Mclchizcdck, 
Hebron,  Joshua  the  Son  of  Nun,  a^id  Caleb  the  Son 
of  'Jej)hunneh,  as  Connected  with  the  Narratives  rC" 
latino  to  these  Personages. 

§  89.     Thus  there  has  been  unveiled,  in  the  opening  of 
Genesis,  the  Parker  and  Metius  forms,  used  in  and  about 
the  construction  of   the   pyramid,  with  also  the  blending 
of  circular  with  square  measure,  by  means  of  the  factor  6. 
So  there  has  been  shown  a   numerical  use   involving,  ex- 
actly, the  scales  of  positive  land  measuring  as  contained 
in  the  British  measures,  founded  on  \}[\Q.sqiiare  inch;  which, 
in  the  pyramid,  is  shown  to  be  the  practical  unit  of  meas- 
ure raised  on  the  source  of  the  cubit  value,  in  the  number 
20612,  a  circular  value,  which,  cubed   and  unfolded,  pre- 
sents the  symbol  of  the  cross.     Undoubtedly  the  work  of 
construction  in  the  Bible  is,  in  sequence,  the  process  of  cal- 
culation of  time  and  distance  running    co-ordinately  to- 
gether with  geometrical  construction,  until  the  perfect  pyr- 
amid is  to  be  found  at  the  period  described  as  that  of  the 
food,  as  will  be  shown.     But,  because  of  inability  to  trace 
clearly  this  building  process,  with  its  detailed  applications, 
another  method  must  be  resorted  to — viz.,  that  of  closing 
back  to  these  conclusions,  by  setting  forth  salient  positive 
exhibitions  of  uses  of  this  system,  which  can  be  found  in 
the  text.     The  exact  method   resting  on  the   Parker  and 
Metius  forms  are  the  furtherest  off,  and  the  most  carefully 
obscured.      On  these,  however,  collaterally,  were  raised 
calendar  systems,  exact  enough,  and  for  general  use,  sub- 
ject to  correction,  at  long  intervals,  by  means  of  the  deeper 
and   more  obscured  knowledge    of    cosmic    construction. 
The   showings  of  both   methods   run    parallel   with    each 
other ;  and  the  commoner  or  calendar  methods  involve  such 


§  89-  Appendix  II.  207 

uses  of  the  other  system,  tliat  their  presentation  will  help 
to  lead  one  to  the  recognition  of  the  elaboration  of  the  pro- 
founder  method.  One  of  the  phases  of  calendar  calcula- 
tion is  so  marked  and  prominent,  so  wide  in  its  limits,  em- 
bracing such  an  extent  of  the  Scripture  narratives,  that  it 
is  well  and  instructive  to  give  it. 

Mr.  John  Bentley,  in  his  Hindu  Astronomy,  sets  forth 
the  war  in  heaven,  as  given  by  the  Hindus,  as  but  a  figure 
of  the  calculations  of  time  periods  ;  and  goes  on  to  show, 
that  among  the  western  nations,  this  same  war,  with  the 
like  results,  took  the  form  of  the  war  of  the  Titans.  This 
was  the  same  (Sir  William  Drummond)  with  the  war  of 
the  kings,  in  14th  Genesis.  All  the  results  are  but  identi- 
cal with  time  calculations  of  the  pyramid,  or  Parker  num- 
bers. The  key  of  the  position  is  in  the  names,  among 
which  the  most  prominent  are  those  of  Adram  and  of  the 
royal  Melchizedec.  The  uses  of  the  numbers  involved  in 
these  names,  to  produce  time  periods,  bring  in  the  Gnostic 
value  of  Christ  in  the  New  Testament,  and  consequently, 
serve  to  show  the  prevalence  of  this  kind  of  knowledge, 
down  to  the  times  of  the  Christian  era.  Mr.  C.  W.  King, 
in  "The  Gnostics  and  their  Remains,"  page  13,  says: 
"  The  relations  of  the  Sephiroth,  or  -.^ons  (Ages),  to  one 
another  the  Kabbalists  represent  by  a  number  of  circles  in- 
tersecting in  a  mysterious  manner,  ad  infinitum,  or  else  by 
the  figure  of  a  man,  or  a  tree,  formed  out  of  such  circles. 
This  figure  of  the  man,  Seir  Anpin,  consists  of  243  num- 
bers, the  numerical  value  of  the  letters  in  the  x\?imQ.  Ahrani 
signifying  the  different  orders  in  the  celestial  hierarchy. 
The  original  idea  was  apparently  taken  from  the  Hindu 
figure  of  Brahma,  and  the  various  castes  typified  by  the 
several  parts  of  his  body  ;  in  fact,  the  names  Abram  and 
Brahma  are  equivalent  in  numerical  value."  From  the 
writings  of  Godfrey  Higgins,  quoting  from  St.  Barnabas, 
it  is  to  be  seen  that  the  value  of  318  was  a  great  value  of 
Christ,  as  was  also  the  number  608.  This  is  to  be  found, 
also,  in  "  CEdipus  Judaicus,"  by  Sir  William  Drummond  ; 
and  also,  as  to  608,  in  the  work  of  Professor  Gustav  Seyf- 


2o8  Appendix  II.  §  89. 

farth  on  "  Chronology  ;"  and  also  in  the  hymn  of  Mar- 
tianus  Capella.  The  318  is  the  same  with  the  318  trained 
or  instructed  servants  of  Abraham,  in  14  Genesis;  or,  as 
by  another  version,  the  318  circutncizcd  xn^n  of  his  house- 
hold. It  is  to  be  found  in  the  same  place,  obscured  in  the 
name  oi  Eliczer  of  Damascus,  or  the  318  of  the  Pit — a  foil 
against  the  promise  of  offspring  that  should  be  the  318  of 
the  vernal  ascendency.  The  value  318  has  reference  to 
the  base  of  astronomical  calculation,  used,  as  shown,  so 
much  in  the  pyramid  numbers,  as  a  diameter  value  to  a 
circumference  of  unity ;  6  times  the  amount  of  which,  or 
318-I-  X  6,  gives  the  height  of  the  king's  chamber,  which 
height  involves  the  square  root  of  the  solar  year,  and  the 
measure  of  that  year  upon  the  celestial  measuring  circle  of 
360°,  as  shown. 

(^.)  Now  the  value  of  the  name  of  Abram,  as  given  in 
the  Hebrew,  is  243,  and  243  is  the  one-half  of  486,  the 
height  of  the  great  pyramid,  in  its  standard  measure,  as 
shown  in  the  text.  This  was  a  sun  measure.  But  a  change 
was  made  in  the  name  of  Abram  to  Abraham  ;  by  which, 
numerically,  5  was  added  to  243,  so — 

Abram  =  243 

Abraham        =  248 

(<5.)  One  Gnostic  value  of  Christ  being  318,  another 
was  608  ;  and  this  last  involves  the  personage  Mclchizedec, 
to  whom  St.  Paul  likens  Christ,  saying  of  him  that  he  was 
a  priest  forever,  without  beginning  or  ending  of  days,  after 
(or  in  likeness  of)  the  order  {ox  number)  of  Melchizedec — 
that  is,  he  was  an  Aeon,  or  oulaum,  or  [see  §  84  {c.)  (i.)] 
porchway  of  the  temple,  or  the  continually  recurring  flux 
and  rebirth  o{  tifne  without  end.  The  Hebrew  word  for 
Melchizedec  is  a  compound  word,  composed  of  ^D/O, 
'•^melchi"  my  king,  and  pllf,  '■'tscdck,''  in  the  construct, 
meaning  the  quality  of  exact  probity,  righteousness,  or  the 
equivalent  exactitude,  rightness.  (He  was  as  Cain,  or 
Vulcan,  Pater  Sadie  the  "Just  One,  holding  the  balance 
of  the  year,  and  the  distributor  of  its  fruits  of  bread  and 
wine.)     The  word  comes  from  a  verbal,  and  has  another 


§  89-  Appendix  II.  209 

co-ordinative  derivative  pHV,  tsadik,  having  the  precise 
same  meaning,  with  one  remarkable  difference  noted  in  the 
dictionary  as  ^^  spec,  mtscrtcors" — that  is,  the  specialty  of 
mercy,  or  pity,  or  forgiveness.  Christ  was  especially 
represented  as  having  all  the  attributes  of  an  exacting 
God,  under  the  law  (so  Paul),  softened  by  these  very  qual- 
ities. 

(i.)  Now,  the  word  Melchize'dek,  or  p1V"*D7D=  40  -f- 
30  +  20  +  10  =  100,  -f-  90  +  4  +  100  =  294,  while  the  cor- 
related exception  of  Melchizadik,  or  pnV"07D  =  40 -[- 30 
+  20  -f-  10  =  100,  +  90  -(-  4  -f  10  -}-  100=  304.  As  seen 
here,  the  word  Melchizedek  can  be  changed  to  Melchiza- 
dik, by  which  change  mercy,  <xx\d  pity,  TxxiA  forgiveness 
are  worked  as  additional  qualities  on  the  first  word,  by  the 
addition  of  the  value  of  10  the  perfect  one.  As  a  fact,  the 
narrative  determines  this  very  change,  for  Abram  is  repre- 
sented as  paying  tithe,  or  the  tenth,  to  Melchizedek,  or  10 
to  the  number  294,  thus  making  it  304.  (Now,  Abraham  is 
represented  as  pursuing  with  his  318,  to  Dan.  But  Dan, 
as  will  be  shown,  is  astronomically  in  Scorpio,  the  zodiac 
sign,  the  gateway  to  the  descendant,  the  place  of  the  cru- 
cifixion of  the  year ;  the  place  where  D-Lilah  received 
Samson  (the  sun)  into  her,  so  represented,  dark  and  treach- 
erous embrace ;  the  place  called  shiac,  ll^t^*,  or  the  pit,  a 
word  from  that  verbal,  the  hifil  participle  of  which  is 
Bfsiach,  TX'^12,  as  he  who  causes  to  go  down  into  the  pit, 
as  here,  astronomically,  for  the  salvation  of  the  world.) 

(2.)  Abratn,  then,  is  243,  the  half  of  the  sun  measure 
486  ;  and  Melchizadik  (the  tithe,  or  10,  being  paid)  is  304, 
the  half  of  608,  or  the  other  Gnostic  value  of  Christ,  or 
M^siach.  Give  the  other  value  as  of  Abraham,  or  248, 
and  make  use  of  the  values  found. 

{a.)     Abram  =  243 

Abraham      =  248 

Make  use  of  these  with  304  X  2  =  608,  the  Christ  value. 

{b.)     608  —  243  =         365; 

or  the  solar  year  value, 

608  —  248         =         360 


2IO  Appendix  II.  §  89. 

— the  value  of  the  celestial  circle  of  three  hundred  and 
sixty  degrees,  or  that  on  zvhich  the  year  is  measurable. 

(c.)  Cassini,  in  the  last  century  (according  to  Godfrey 
Higgins),  discovered  the  great  cycle  of  600  years  as  be- 
longing to  the  Hebrews,  as  well  as  to  Hindus  and  Siamese, 
and  shows  that  Eusebius'  (who,  with  Constantine,  secularly 
founded  the  Christian  Church)  chronology  agrees  with  its 
use.  It  is  the  great  divine  avatar,  or  incarnation  period. 
The  greatness  of  its  value  consists  in  the  fact  that  it  serves 
to  measure  the  time  of  conjunction  of  the  sun  and  moon  in 
the  heavens,  in  the  same  -place,  by  recurrence ;  whereby, 
by  astrology,  a  new  birth  should  ensue.  Cassini  said  of 
this,  that  it  was  one  of  the  finest  astronomical  periods 
known,  and  worthy  of  all  praise.  It  is  one  that  remains 
perfect  from  cycle  to  cycle,  by  the  intercalation  of  i.-|-  days 
in  600  years. 

(i.)     Here,  again,  the  pyramid  values  come  into  play, 

for   190. 9853+,   the    numerical  value   of  the  —  base  side 

of  the  pyramid,  or  10  times  the  height  of  the  king's  cham- 
ber, or  31.8,  the  Christ  value,  X  6,  is  the  diameter  to  this 
very  value  as  a  circumference.  So,  also,  as  a  straight  line 
value,  it  is  represented  for  circumference  by  1130.98  -f-  6. 
(i/.)  Now,  Godfrey  Higgins  finds  608,  also  a  cycle  in- 
dex, connected  under  the  system  with  that  of  the  600,  and 
attributes  the  difference  to  difference  of  value  of  precession 
of  the  equinoxes  discovered.  But  in  this  he  seems  to  lack 
strength  of  proof.  Cassini,  as  has  been  said,  showed  the 
value  of  the  600,  as  co-ordinating  lunar  with  solar  cycles. 
If  you  wish  to  measure  solar  time  as  of  days  in  the  year, 
for  600  years,  on  the  great  circle  of  360°,  the  formula  will 
run — 

(i.)     365  -  X  600  =  360  X  608+ ; 

whereby  the  608,  or  Christ,  or  Melchizadik,  value  becomes 
a  measure  of  transfer,  or  of  equivalence  of  solar  time  into 
the  division  of  the  zodiac  into  degrees.  Hence,  both  these 
personages,  under  the  number  form,  were  means  of  meas- 


§  8g.  Appendix  II.  211 

lire  of  transfer  of  solar  time  in  days  into  degrees  of  the 
time  circle. 

(c.)     Here,  however,  it  will  be  said,  or  objected,  that  a 
foreiern  value  has  been  introduced  to  bring  about  this  re- 

suit,    viz.,  -  of  a  day  has  been  added  to  the  365  obtained 

4 
by  the  use  of  Abram  and  Melchizadik — that  is,  that  the 

3'ear  is  now  used  as  corrected  in  the  calendars,  viz.,  by  the 
intercalation  of  i  day  in  4  years ;  or,  by  another  showing, 
to  365  X  4=  1460  days,  one  day  has  been  added,  making 
the  period  that  of  the  bissextile^  or  leap  year,  or  a  full 
period  of  1461  days.  This  is  true;  and,  true  to  the  need, 
this  very  correction  is  provided  for,  and  most  prominently 
marked,  in  the  -place  of  residence  of  Abram,  which  was 
Hebron,  formerly  called  Kirjath-Arba — which  latter 
name  means  the  city  of  4. 

Hor  Apollo  says  :  "  They  (the  Egyptians)  further  rep- 
resent it  (the  year),  by  a  quarter  of  an  acre,'"  or  aroura ; 
and,  "  The  acre,  divided  \n\.o  four,  denotes  the  bissextile 
paiiod  o(  four  years"  (Volney's  Ruins,  page  134).  It  is 
thought  that  this  is  also  noticed  by  Professor  Seyfl'arth.  So, 
the  city  of  ^,  or  Hebron,  or  Kirjath-Arba,  the  place  of 
Abram's  residence,  would  serve  to  denote  the  measure  of 
the  bissextile  year,  and  was  thus  the  proper  place  of  resi- 
dence of  Abram,  the  sun  measure.  When  the  .three  men 
(angels)  came  to  see  Abram,  he  was  seated  in  the  opening 
of  his  tent,  representation  of  the  pyramid,  the  time  being 
spoken  of  as  midday.  Here  was  the  sun  directly  over  the 
apex  of  the  pyramid,  of  which  the  height  was  indicated  by 
243.  The  contrast  of  this  kind  of  measure  is  in  Lot, 
Abram's  brother,  being  seated  in  the  gates  of  darkness,  or 
Sodom,  or  woman's  lust,  at  evening.  (There  is  a  very 
curious  affinity  between  the  words  for  Hebrew,  for  Hebron, 
or  rather  Chebron,  and  iox  Hebron.  The  word  for  Hebrew 
is  'yy^,  which,  as  ober,  means  to  pass  over;  but,  also,  a 
imion,  a  joining  together — and  this  word  equals  Hebcr,  or 
Chcber,  ")2n,  whence  Hebron  or   Chebron,  the  residence 


212  Appendix  II.  §  89. 

of  Abram  :  but  this  is  in  affinity  with  Hcber^  "IDH,  "  to 
divide  in  pieces;  hence,  figuratively,  to  divide  off.,  to  de- 
termine the  heavens,  after  the  manner  of  astrologers." 
Hence  the  glyph  of  Hebron,  as  a  united  yet  parceled-off 
heaven,  appears  in  the  run  of  the  word.) 

( /.)  But  the  above  statement  does  not  rest  for  its  sup- 
port upon  its  intrinsic  strength,  or  upon  its  curious  fittings 
in  the  connections  made.  It  is  fully  confirmed.  Of  the 
children  of  Israel  who  left  Egypt,  only  two  were  permitted 
to  enter  the  promised  land.  One  was  Joshua,  the  son  of 
Nun,  or  of  the_;f5/^,  and  the  other  was  Caleb,  the  son  of 
Jc-phiinneh,  or  the  dog  the  son  of  the  female  dog.  Both 
were  astronomical  types.  (Nork,  in  Worterbuch,  says  that 
Joshua  ...  is  the  biblical  ^sculapius  soter,  inas- 
much as  ^sculapius  had  the  dog  for  a  companion,  even  as 
Joshua  had  Caleb  (the  dog)  ;  also  Hermes  Kunocephalus, 
\\iQ.  fire  dog  \x\.  the  summer  solstice,  in  the  month  of  the 
lion,  when  Sirius  rises  heliacally  with  the  sun,  and  dogs 
are  offered  to  ^sculapius  ;  for  Caleb's  father  is  the  solstice, 
or  turning-man  (11^5%  Strophios,  Vergilius),  and  to  the  dog- 
headed  Anubis  the  predicate  Strophaios  [hinge)  belonged.) 
Joshua  was  a  type  of  the  sun,  and  Caleb  was  a  type  of  the 
great  cycle  of  the  sun,  which  cycle,  as  the  Sothic  period 
among  the  Egyptians,  was  marked  by  the  rising  of  Sirius, 
the  dog-sidiV,  in  Egypt,  heliacally  with  the  sun.  (Joshua, 
as  fsh,  was  also  a  Jehovah  numerical  form,  for  Nun,  fish, 
is  pj  =  565  ;  and  the  Jehovah  form  is  56.5  X  10=  mr7* 
=  565  =  also,  113  X  5.)  The  Sothic  period  was  that  of 
the  vague  year  of  365    days,  corrected  to  the  true   solar 

value.     Falling  back — of  a  day  each  year,  in  1461  years 

the  correction  would  take  place,  by  dropping  a  vague  year 
from  the  count ;  it  being  simply  an  enlargement  of  the  bis- 
sextile correction  of  1460  and  1461  days  in  the  period  of 
four  vague  years.  So,  Caleb  was  the  dog,  sure  enough  ; 
but  he  was  the  dog-star,  to  determine  a  point  for  bis- 
sextile correction,  or  for  correction  of  the  Sothic  period  or 


§  89.  Appendix  II.  213 

cycle.  When  he  entered  the  promised  land,  where,  in  it, 
was  his  possession  assigned  to  him?  Why,  of  all  places, 
he  was  assigned  just  that  one  that  proves  all  that  has  been 
said — viz.,  Hebron,  ox Kirjath-Arba,  the  city  0/ ^,  the  resi- 
dence of  Abram  the  sun  measure,  significant  of  the  bissex- 
tile correction  in  days  of  1461  for  1460,  and  of  the  Sothic 
cycle  correction  of  1461  for  1460  years  :  "which  place,"  the 
record  goes  on  to  state,  "  before  that  time,  was  Kirjath- 
Arba,  which  mafi  was  great  among  the  Anakims."  That  is, 
the  c/iy  of  4,  which  {tnan,  or  113  circumference  to  36,  or  4 
squares  of  6  X  6  each,  for  the  city  of  4),  was  great  among 
the  cabiri,  or  stroiig  ones  (Gibborim),  or  planets,  or  cycles, 
for  the  correction  of  their  recurring  periods. 

A  hint  is  observable  in  the  Biblp  as  to  indications  of  time 
cycles.  '"'- Enoch  ^''  connected  with  the  year  circle,  '■'■walked 
with  God,  and  he  (was)  not:  for  God  took  him."  Noah 
was  "  perfect  in  his  generations  ;  Noah  walked  with  God." 
Noah  was  pre-eminently  a  period  marker.  ^^IIeb?'on, 
therefore,  became  the  inheritance  of  Caleb,  the  son  of 
Jephunneh,  the  Kenezite,  unto  this  day;  because  that  he 
wholly  followed  the  Lord  God  of  Israel;"  and  Caleb  was 
the  detcrminaior,  by  correction,  of  the  leap  year  and  the 
Sothic  period.  Of  Melchizedek  (Pater-Sadic),  Hebrew 
learning  has  handed  down  that  he  was  without  beginning 
or  ending  of  days.  True,  but  he  was  a  means  also  of  de- 
termining both  by  correction,  holding  the  balance  of  the 
ecliptic.  (As  to  the  value  of  Melchizedek  of  294,  this  is 
49  X  6 ;  and  as  to  the  number  49,  or  7-,  attention  is  called 
to  "Proposition  2,  Theorem,"  and  to  "Proposition  3, 
Theorem,"  of  a  "  Quadrature  of  the  Circle,"  and  "The 
Square  Root  of  Two,"  by  W.  A.  Myers,  of  Louisville, 
Ky.  (Wilstach,  Baldwin  &  Co.,  Cincinnati.)  It  may  be 
that  Mr.  Myers  has  reproduced  an  ancient  method  for  the 
calculations  of  circular  elements  as  sines,  cosines,  etc. 
His  Proposition  3  is  as  follows  : 

"  ( I .)  If  a  circle  be  described  with  the  square  root  of  two  for  a  ra- 
dius, and  the  onc-fftictJi  of  the  square  described  on  the  radius  be 
deducted  therefrom,  the  square  root  of  the  remaining  ybr/j'-w/w*; 
fftictJis  can  be  extracted  exactly.     (2.)  The  square  root  of  the 


214  Appendix  II.  §  90. 

— so  deducted  will  be  the  sine  of  the  given  arc.     (3.)  The  square 

root  of  the  remaining:-'^  will  be  the  cosine  of  the  eiven  arc." 

In  many  respects,  his  work  is  well  worth  attention.) 
§  90.  Commentators  are  struck  with  the  marked  simi 
larity  of  the  histories  of  the  lives  of  Abram  and  Isaac. 
They  seem  to  be  phases  of  some  one  underlying  subject- 
matter.  Suppose  this  to  be  so,  and  that  this  subject-matter 
is  astronomical,  or  numerically  connected  with  astronomy; 
then  it  is  observable  that  the  age  of  Abram,  or  175  years, 
added  to  the  age  of  Isaac,  or  180  years,  amounts  to  just 
355,  the  Hebrew  word  for  year,  or  shanak,  or  H^JT ;  and 
also  the  circumference  of  a  diameter  of  113,  together  the 
Garden  of  Eden  measures.  So  Abram  and  Isaac,  together, 
are  but  one  circumference,  and  that  a  year  circle,  for  as- 
tronomical determinations. 

Take,  therefore,  the  calendar  keys  here  presented  in  the 
showing  of  the  bissextile  and  Solhic  cycle  correction.  As 
a  whole  there  is  355  the  combined  value  of  Abram  and 
Isaac,  the  abstract  circumference  value  of  which  113  is  the 
diameter.  113  is  ma7i,  and  from  him  in  the  Garden  is 
worked  out  the  connected  Parker  form  of  6561  :  20612, 
with  other  uses.  While  113  is  7nan,  however,  355  is  the 
Hebrew  word  shanak,  or  year ;  and  here,  in  Abram-Isaac, 
the  man,  355,  as  tho.  year,  eventuates.  But  with  Abram  as 
part  of  this  year  value,  the  natural  year  of  365  days  is 
worked  out,  and  also  its  measure  circle,  360  degrees.  But 
360  was  also  with  the  ancients  a  year  day  value.  So  there 
is  elaborated  in  this  use  three  year  day  values — 

(I.)  355  360  365; 
where,  by  the  order,  and  very  relation  shown,  the  reason 
of  the  form,  as  applied  to  time  measure,  is  shown  ;  for  it  is 
a  comparison  of  an  abstract  circtimference  value,  355,  with 
the  natural  year  value,  365,  and  is  also  connected  with  it 
by  use  of  another  jy^ar  value,  360,  which  is  also  a  celestial 
and  geographical  measure.  The  beauty  of  the  form  con- 
sists in  this,  that  360  is  the  mean  between  the  abstract  and 
natural  year  circle  value. 


§  90-  Appendix  II.  215 

It  is  seen  that  while  ordinary  calendar  systems  can  be 
formed  on  this  form,  so,  also,  it  links,  in  355 >  with  the 
forms  for  exact  cosmical  determinations. 

Now,  with  the  ancients  the  picture  of  a  year  was  of  a 
serpent  swallowing  the  end  of  his  tail  (or  one  or  more  units 
of  its  length).  Take  the  woman  form  of  time  production. 
It  is— 

(2.)  7  X  4  =  28,  and  28  X  13  =  364, 
and  this  is  the  luni-solar  year  day  value.  This  is  seen 
to  be  one  day  less  than  365,  the  vague  year  day  value.  A 
serpent  of  365,  then,  swallowing  i  unit  of  its  length  would 
symbolize  the  expression  365-1,  or,  in  Hebrew,  C^I^K,  or 
Enosh  son  of  Scth,  the  son  of  man  (Daniel),  or  the  com- 
bination of  the  two  kinds.  By  sympathy,  355  would  take 
the  same  form  as  365-1  :  so  the  numerical  formulation 
for  the  different  year  values,  combined  into  a  system, 
connecting  itself  with  land  measures,  and  pyramid,  and 
Garden  of  Eden,  and  temfle,  and  tabernacle,  construc- 
tion, would  be — 

(3-)        355  ^     360     r  365 
I     (        I        )     I 

354  )     359     (  364 
In  truth  and  in  fact,  while  355,  or  shanah,  is  the  Hebrew 
word  value  for  year,  the  true   Hebrew  and  ancient  year 
value  of  this  kind  was — 

(4-)  355  —  I  ==  354  days. 
And  here  its  origin  is  laid  bare.  So,  also,  the  working  of 
the  woman  sexual  form  of  the  garden  is  seen  to  harmonize 
with  every  other,  or  connect  with  every  other.  In  truth,  in 
calendar  calculations,  the  woman  sexual  use,  under  the 
number  7,  seems  to  have  been  a  fundamental  one.  It  is 
true,  too,  that  while  the  Garden  of  Eden  involves  355 
through  113,  so  it  has  also  reference  to  this  very  value 
354  as  a  circumference  instead  of  355,  or  as  well  as  355. 
Take  the  form  113  :  355,  multiply  by  5,  and  there  results 
565  and  1775.  But  take  355  —  i  =  354  and-multiply  by  5, 
and  there  results  177-0.  Now,  by  adding  the  yv^// values 
of  the  letters  in  the  words   Garden   Oden,  or  pI^-3-3,  and 


2i6  Appendix  II.  §  90. 

there  results  3  +  50  =  53,  +  70  +  4  H-  50  =  177  ;  which  is 
significant  of  this  change,  for  177  ~^  5  =  35  •4-  Strange  it 
is  that  bend  this  into  the  form  of  a  circle,  and  354  may  be 
read  345,  which  is  the  name  Moses,  111^0,  or  345.  But 
this  name  seems  rather  to  have  reference  to  the  radius 
value  of  circular  elements  (3.)»  §  82,  having  reference  to 
the  interior  works,  of  calculation  of  astronomical  admeas- 
urements, in  the  great  pyramid. 

Uses  of  and  developments  of  this  form  (3.)  will  be 
shown  hereafter,  with  confirmations  as  to  its  ancient  recos- 
nitions. 


§  pi.  Appendix  III.  217 


APPENDIX  III. 

The  Word,  or  Logos,  connecting  with  yohn,  or  Jonah, 
or  Dove,  with  "J-hovah,  and  with  "Jcs-us,  through  the 
Fish. 

§  91.     {ai)  Attention  is  desired  to  the  formula  of — 

12  4  ^   ^^ 

(I.)     206.  —  feet,  x—=  274.8266, 

o 

as  arising  from  the  original  Parker  formulation  of — 

(2.)      20612  X  —=  27482.66+, 
o 

in  §  78  (c.)  (3.),   valuable   as   giving  the   standard  height 

from  the  base  of  the    pyramid  of  137.4132-}-  feet,  -f-  the 

standard  height  of  the  king's  chamber  region  of  68.7068 

12 
feet,  equal  to  206.  — feet;  or  80  cubits  +  40  cubits  =120 

cubits  :    and  also    developing  the   same  measure  in    §  78 

(6.)  (2.),  in  274.826 — 2o6.i2  =  68.7o6-f-feet,  or  the  king's 

chamber  region. 

The  use  is  the  origin  of  measure   20612,  where  it  is 

12 
worked  into  2,  foot  and  cubit  y\\wQ  of,  respectively,  206 

feet  and  120  cubits,  to  obtain  a  form  of  measure  for  regu- 
lating the  interior  works  of  the  great  pyramid,  having 
reference  to  the  comparison  of  lunar  with  solar  time,  and 
the  correlation  of  distance  measure — all  cosmical,  or  of 
divine  adjustment.  It  is  seen  that  the  form  retains,  numeri- 
cally, the  origin  of  measure,  in  the  abstract  number  20612, 

then  uses  it  as  20612  inches  (seen  in  §  78),  then  as  206 — 
feet,  which  is  120  cubits.  In  120  cubits  there  is  the  num- 
ber 12,  or  6 -{-6,  the  means  of  application  of  the  Parker 
forms  to  earth  measures;  which,  as  composed  of  6,  is  in- 
dicative of  the  change  worked  on  the  standard  measures  to 
obtain  actual,  or  real  pyramid  measures  :   for  6  is  circum- 


2i8  Appendix  III.  §  91. 

ference  to  the  well-known,  number  i. 90985 -f.     This  con- 

12 
dition,  then,  of  the  number  form,  as  of  206 -feet,  or  120 

cubits,  is  a  great  controlling  one,  as  at  the  base  of  cosmic 

and   earth   measures,    in    construction.      In  this   form   of 

^  12   .  .  .12 

206. —  it  carries  the   decimal    —  as  implied ;    that  is,  to 

100  ^ 

express  the  value   120  cubits,  one  would  say,  "It  is   206 

feet,"  meaning,  or  intending  to  mean,  the  exact  value  of 

12 

206  feet  and of  a  foot.     This  numeral  206,  thus  used, 

100  ' 

gives  the  interpretation  of  the  great  word  L,ogos,  or  The 
Word,  used  so  mysteriously  in  the  Scripture.  This  is  from 
and  but  another  form  of  the  Hebrew  word  'y^'^,  ddbvar,  or 
word.  Kabbalistically  it  was,  that  by  the  Word,  or  dabvar^ 
God  created  all  things.  The  value  of  ddbvar  lays  in  the 
numerals,  or  values  of  its  letters,  which,  added,  are 

206, 
having  reference  to  the  perfect  circumference  20612,  under 
the  form  of  that  part  of  the  expression — viz.,  206,  used  as 
a  whole  number,  in  feet,  for  the  expression  of  120  cubits. 

The  New  Testament  being,  after  all,  but  an  unfolding 
of  the  mysteries  of  the  Old,  under  another  dress,  is 
the  best  illustrator  we  have  of  the  mysteries  outside 
of  the  ancient  books ;  the  Hebrew  Kabbala  being  of 
less  use,  because  of  the  care  used  to  conceal  its  teachings. 
Therefore,  the  New  Testament  can  be  resorted  to,  to  ex- 
emplify and  teach  the  hidden  wisdom  of  the  Old.  What 
is  stated  as  to  this  value  (which  also  implies  the  Jehovah 
value  of  a  one  of  the  denomination  of  20612)  is  exempli- 
fied in  the  opening  passage  of  the  Gospel,  ^^  according  to 
{or  agreeing  with)  yohn;"  premising  that  the  Greeks  trans- 
lated Elohini  by  Thcos,  and  'Jehovah  by  Ktcrios,  as  the 
English  do,  respectively,  by  God  and  Lord.  This  opening 
sentence  is  a  type  of  the  opening  sentence  of  the  first  verse 
in  Genesis.     John  says  : 

"/«  the  beginning  was  the  Word,  and  the  Word  was 
with  God,  and  the  word  was  God."'' 

It  has  been  seen  that  the  word  Elohim  stands  for  the  re- 


§  91-  Appendix  III.  219 

lation  of  31415,  or  circumference  value  to  i,  or  diameter  of 

unity.     Now,  the  Word,  or  Ddbvar,  its  Hebrew  prototype, 

is  the  expression  of  a  whole  number  of  120  cubits,  under 

12 

the  value   of  206  feet  and of  a  foot.     It  thus  carries 

100 

with  it  the  numerical  value 

20612, 
or  the  value  of  a  perfect  circumference,  raised  to  just  that 
value,  on  which  such  sublime  results  as  have  been  traced 
could  be  produced. 

John,  then,  was  simply  setting  forth  the  law  of  creation, 
in  the  terms  of  31415,  or  circumference  to  a  diameter  of 
unity,  raised  to  this  very  form  or  value.  The  Word,  then, 
as  20612,  was  but  a  play  upon  Elohhn,  or  God,  as  31415' 

'John  the  same  with  Jonah. 

(d.)  The  use  of  the  name  ^'John,"  as  this  opening  sen- 
tence is  '■'■  according  to  John,''  is  perfectly  appropriate  to 
the  expression;  for  John,  in  Hebrew,  is  H^V,  or  Jonah. 
The  value  of  the  name,  adding  the  letter  values,  is 

71; 
or  the  -  of  355,  the  circumference  of  113  (which  raised,  as 

stated,  is  a  Jehovah  value).     So  that,  while  the  Word  im- 
plies the  relation  20612  :  6561,  John  shadows  forth  that 

of  113  :  355. 

Th c  Word  '^  Begin n ing. " 

(c.)     The  word  '■'beginning''''  is  also  appropriate  in  the 

connection,  and  is  here  as  the  first  word  in  Genesis.     It 

is  used  for  the   equivalent  Hebrew  word  V^TS,  rash,  for 

head,  or  substance,  or  beginning.     The  value  of  the  word, 

in  Hebrew,  is  213,   and  is  equal  to  355  X  6  =  213-0:  so 

that  John,  or  71X5  =  355,  and  this  X  6  =  213-0,  or  be- 

ginning,  or  head. 

John  and  Jonah  as  Dove. 

(d.)     This  word   John,  in   Hebrew   Jonah,  is  also  the 

Hebrew  word  for 

Dove, 


220  Appendix  III.  §  91. 

which  last  word,  as  used  in  the  description  of  the  flood, 
symbolized  the  use  of  this  very  circumference  value  of  355, 
because,  it  will  be  seen,  on  the  reading  of  the  narrative, 
that  the  word  is  used  in  the  connection  just  5  times,  or  in 
all  71  X  5  =  355-  For  this  reason,  with  others,  it  became 
one  of  the  greatest  symbols  among  all  the  ancients. 

The  Fish,  as  connected  with  the  Dove,  or  'John,  or  Jonah. 

(^.)  By  a  most  curious,  but  exquisite  use,  this  word 
Dove,  thus  indicating  a  circumference  value,  was  made 
convertible  into  a  diameter  value,  through  the  intermedia- 
tion of 

The  Fish; 
of  which  Joshua  was  the  son.  The  relation  of  this  word 
jish  to  the  divinities  is  also  not  only  to  be  found  among  the 
records  of  the  heathen,  but  at  the  base  of  the  Christian 
Books.  One  derivation  of  its  value  is  from  a  mathematical 
postulate,  that  any  two  quantities  which,  relatively,  are 
equal  to  a  third,  are  equal  to  each  other.  The  Hebrew  for 
jish  is  pj,  nun  (the  ecclesiastical  English  word  nun,  a  fe- 
male devotee),  and  giving  the  values  of  the  letters  as  they 
run,  the  power  of  the  word  is 

56s 

But  the  word  for  woman,  or  Fve,  or  the  feminine  part  of 
J-hovah,  is  HIH,  and,  giving  the  values  of  the  letters  in 
the  same  way,  the  word  and  value  is 

565 

mrr. 

Thus  it  is  seen  that  nun,  jish,  becomes  equal  to,  and  thus 
is  the  same  with  Eve,  the  woman,  or  hovah,  or  mil,  the 
feminine  part  of  J-hovah,  as  a  diameter  value,  because 
113  X  5  =565  (which,  by  change  of  enlargement,  as  seen, 
becomes  circumference  to  a  diameter  of  36).  Now,  place 
the  numerals  over  the  letters  of  the  word  John,  or  Jonahs 
or  Dove,  as 

5561 


§  91.  Appendix  III.  221 

and  it  is  seen  tliat  all  the  values  of  J-hovah,  as  565',  are 
used,  but  the  arrangement  is  changed  in  the  last  part  of 
the  word  as  to  the  order  of  the  number  hovak,  or  565,  leav- 
ing the  ♦,  or  I,  or  10,  which  is  the  y,  or  yah,  of  y-hovah, 
standing  isolated.  If,  therefore,  the  fish  swallows  the 
word,  and  casts  it  up  from  its  belly,  it  symbolizes  a  birth 
of  the  subject-matter  in  the j^5//  or  nun  form,  or 

556  becomes  565  ; 
or  the  dove  as  71  X  5  =  355  5  a  circumference  value,  is,  by 
use  of  the  fish  as  a  womb,  or  flux,  made  to  assume  the 
value  of  a  diameter  to  this  very  circumference,  for 

113X5  =  565- 
To  565  as  the  re-arrangement  of  the  556  of  the  fish  form, 

or  birth,  add  the  head  of  the  word — viz.,  the  y,  or  yah^  or 
male  part,  which  has  suffered  no  change — and  now 
Jonah,  or  John,  or  Dove,  as  556-1, 
becomes  J-hovah,  as  565-1. 

So  much  for  the^/f^/^  or  nun  use.  (When  John,  or  Jonah, 
or  Dove,  Baptist,  was  beheaded,  his  head,  or  ^  or  jod,  was 
delivered,  or  added  to,  the  woman,  or  hovah,  whereby,  by 
typical  change,  she  became,  gnostically ,  J-hovah  ;  but  his 
body,  or  556,  or  his  equivalent  hovah  part,  was  buried  in 
mother  earth,  or  went  into  the  gate  of  Scorpio,  or  the 
womb,  or  the  fish's  mouth,  which  of  itself  was  hovah  sym- 
bolically carrying  the  phallus  concealed.  It  was  but  a  play 
upon  these  types.  Astronomically,  also,  while  J-hovah 
stood  as  the  emblem  of  the  complete  circle  of  the  sun's  cir- 
cuit, or  the  year,  the  y,  or  ♦,  represented  \\\q.  power  of  the 
sun  above  the  equinoxes,  while  the  hovah,  or  female  part, 
represented  all  below,  as  the  winter,  or  water,  part.  So, 
yacoh,  the  heel,  §  92  {b^,  after  his  before  morning  struggle 
with  that  angel,  who  was  Esau,  passing  upward,  had  his 
name  changed  as  the  morning  sunbeams  fell  upon  him. 
He  changed  his  before  feminine  qualities,  and  now  became 
yes — 213;  i.  e.,  "ijj^^-j^^  =  Jes-rael,  or  yt:5-us  head^'^LS 
the  Greeks  would  have  had  it.  The  mark  of  separation 
between  the  two  conditions  was  the  brook  Penuel  or  Jab- 
bok.     A  very  happy  illustration  of  the  dove  and^fs/^  use  to 


222  Appendix  III.  §  91. 

make  'Jcho'vah  can  be  given  from  ancient  sources.  "The 
Syrians,  or  Phenicians  (says  Nigidius),  assert  that  a  dove 
sat  several  days  in  Jiic^hrates  (one  of  the  rivers  of  the 
Garden)  on  tlie  egg  of  a  Jish,  whence  Venus  was  born." 
(Note  to  Volney's  Ruins,  p.  168.)  Here  the  whole  trans- 
formation is  shown  by  symbol.  The  result  is  ivonian  as 
Venus,  the  primal  conceptio7i,  or  jlin,  or  Eve,  which  is 
113  X  5  =565,  concealing,  as  shown,  a  man  value]  the 
whole  being  mn*.) 

The  Te  Deutn  and  the  Birth  of  the  Savior. 

(_/".)  The  early  church  recognized  just  such  uses,  as  can 
be  gathered  and  shown  from  Clemens  Alexandrinus.  Nor, 
indeed,  was  there  any  departure,  in  so  doing,  from  the  most 
perfect  reverential  observance.  In  the  Te  Dciim,  a  song 
of  praise  to  the  Deity,  in  the  recognition  of  His  works,  it 
says  :  "  We  praise  thee,  O  Elohim!  ive  acknozuledge  thee 
to  be  the  Jehovah."  Then,  speaking  of  the  Savior,  it  is 
averred  that  He  was,  as  a  man,  not  only  born  of  a  woman, 
but,  further,  that  that  woman  was  a  virgin.  How,  then, 
could  such  a  thing  be,  consistently  with  the  truth  and  the 
laws  of  nature.  It  has  been  seen  that  the  woman  could  be 
truthfully,  and  most  perfectly  mathematically,  taken  as  a 
rib  from  the  side  of  a  man,  without  the  exercise  of  any 
natural  procreative  function  ;  and,  in  fact,  from  the  same 
source,  it  was  just  as  easy  to  produce  man,  or  aish,  or  Jes, 
from  the  woman,  by  the  slightest  possible  use  of  change. 
The  woman,  as  coming  from  the  man,  or  ^113,  was 

5315; 
but  if  man  is  to  be  restored  from  the  tlements  of  the  wojnan , 

add  the  values  of  the  letters  composing  her  name,  and  there 

results  n  =  5 ,  +  J^  =  300,  _f-{<=i,-|-rr  =  5,  =  a  total  of 

311.     Now,   C^*N,  7nan,  is,   adding   the  values,   ^  =  300, 

+  *>  =^  10,  -f-  }<=  i,  =  a  total  of  311  ;  or,  reading  the  values 

as  the  letters  run,  the  value  is  113.     The  woman  then  is, 


§  91'  Appendix  III.  223 

in  this  phase,  311,  or  man.     Place  her  thus,  with  man  as 
113,  and  they  stand  face  to  face 

311— 113, 
just  as  they  are  described  in  Genesis.  Thus,  however,  it 
is  seen  how  the  7nan,  ycs-wa,  could  be  born  of  a  virgin. 
But  so  born,  he  is  as  aish,  also  113,  and  113  X  5  ^565,  or 
nun,  who  was  the  mother  of  Joshua  the  Savior.  As  to  the 
first  expression — viz.,  "We  praise  thee,  £/o/iim ;  we  ac- 
knowledge thee  to  be  the  'Jehovah'''' — it  symbolically  be- 
comes, "We  praise  this  principle  of  i  :  31415,  of  which 
the  working  values  are  56,5  X  '^  =  mfl*,  or  113  X  5  =  565  ; 
or,  in  the  other  form,  as  exhibiting  a  perfect  one,  straight 
line,  of  a  denomination  of  20612,  the  perfect  circumference. 


The  Dove  tiscd  in   Calculations  of  the  Year, 
(g:)     The  dove  was  one  of  the  divinity  emblems  through- 
out antiquity,  in  its  character  of  71,  as  the — of  355.     The 

calculations  of  time  for  the  solar  year  sprung  from  the 
taken  value  of  the  lunar  year,  which  word  in  Hebrew  was 
Shanah,  or  H^ti*,  the  value  of  which  was  355.  It  is  pre- 
cisely the  same  whether  a  circle  of  355  is  exhibited  divided 
into  subdivisions  of  5  each,  of  which  the  factor  will  be  71  ; 
or  whether  the  original  circle  be  taken  as  71,  or  the  dove, 
which,  by  subdivision,  as  355  will  exhibit  the  same  ulti- 
mate subdivision  by  5.  In  fact,  the  values  70,  71,  72,  and 
73,  were  famous  values  as  denoting  70  x  5  =  35o»  7^X5 
=  355'  72X5  =  360,  and  73X5  =  365-  The  ancient 
method  of  symbolically  exhibiting  the  year,  was  by  a  ser- 
pent swallowing  one  or  more  units  of  its  length.  Take  71 
as  the  value  of  the  circle  to  obtain  the  lunar  year.  Let  it  be 
subdivided  into  71  X  5  =355  parts,  or  Shanah.  Bendtiiis 
into  the  form  of  a  circle,  represented  by  the  serpent  swal- 
lowing one  unit  of  this  amount,  and  the  resulting  value  is 

354; 
which  was  the  universally  accepted  value,  anciently,  of  the 

lunar  year.     And  this  was  because  it  correlated  the  human 


224  Appendix  III.  §  91. 

method  of  obtaining  this  vahie,  viz.,  52  X  7  —  364?  which 
is  365  —  I  =  364  ;  and  to  compare,  or  correlate,  355  —  i  = 
354.  These  interpretations  are  interesting  as  unravehng 
the  meaning  of  the  source  of  ancient  mythology,  and  as 
showing  a  common  possession,  and  common  origin,  as 
stated  by  Clemens.  By  tradition,  the  origin  of  religion  in 
Greece  was  held  to  have  been  by  the  introduction  from 
Egypt  of  two  black  doves.  By  the  change  worked  on  the 
dove  value  by  the  fish,  two  doves  would  become  two  fishes 
as  565,  and  565,  the  zodiac  sign  of  the  fish  month;  or  like 
use  could  be  made  of  the  value  71,  through  circumference 
values,  etc. 

New   Testament   Use. 

(Ji.)  In  the  Christian  form,  the  man,  or  aish,  or  t^•*^{, 
(this  form  gives  the  other  of  yes,  from  C*%  or  in  Greek  or 
English  Jes-us,  signifying  the  Jirc,  or  sun,  or  Deity,  or 
man.  This  word  by  the  masoretic  points,  which  point  al- 
most undoubtedly  to  the  true  former  pronunciation,  was 
pronounced  t^*J<,  or  ish,  or  Jcs,  for  man;  the  feminine 
form  was  PfCJ^,  or  Issa,  or  woman,  or  Egyptian  Isi-s,  Isis. 
A  collateral  form  was  ^Ji'%  or  ycsse,  or  Isi ;  feminine 
Egyptian,  Isi-s.  But  Isi  vvas  Jesse,  the  father  of  David, 
who  was  the  father  of  Jesus,  as  Isi.  So,  indeed  Isis, 
Egyptian,  was  the  feminine  form  of  Isi,  or  yes-,  He- 
brew, as  a  form  of  aish,  man,)  was  yes-us.  But  an- 
other form  for  Jesus  was  by  Christian  tradition,  and 
Gnostic  use,  Ichthus,  the  Jish.  Now  the  river  Jordan  is 
derivable  from  the  Hebrew  11*,  yared,  to  descend,  jlow 
down;  hence,  river,  with  an  appended  ^,  or  n,  or  nun,  or 
Jlsh;  or  by  name  and  determinative  \it{\.<t\',  Jish-river :  or 
it  may  be  taken  as  lar-Dan,  or  ^''-lar,  and  p,  Dan,  or 
the  river-Dan.  Jesus  the  man  descended  into  and  stood 
in  the  waters  of  this  river  Dan,  ov  Jish.  Now  in  fact  both 
Dan  and  Jish  symbolized  the  same  thing.  The  zodiac  sign 
of  the  tribe  of  Dan  was  in  Scorpio ;  and  to  the  tribe  of 
Dan  was  geographically  assigned  the  place  Dan,  embrac- 
ing the  sources  or  springs  of  the  river  Dan,  which,  as  com- 
ing up  out  of  the  nether  world,  was  the  manifestadon  of  the 


§  gi.  Appendix  III.  225 

fabled  river  Styx.  So,  indeed,  as  it  signified  the  place  of 
entering  another  condition  of  existence  by  death,  it  also 
represented  the  allied  condition  of  a  new  birth.  So  ycs-us, 
the  man,  descending  into  the  waters  of  this  river  Dan, 
Scorpio,  ov  gate  of  the  woman,  where,  by  a  new  birth,  "  I 
await  thy  salvation,  O  Jehovah"  (Gen.  49,  18),  was,  as  to 
his  body,  become  ixjish,  or  nun,  whereby  the  w«;/  becomes 
ychovah.  But  in  standing  in  the  water  the  body  is  the 
fish,  or  in  the  fish's  mouth,  while  the  head  is  the  ♦,  or  num- 
ber 10,  or  a  circumference  to  a  diameter  of  318-}-,  which 
number  was  a  Gnostic  value  of  Christ.  But  who  causes 
him  to  go  down  into  the  water?  John,  or  Jonah,  or  Dove. 
And  here  the  transformation  is  gone  through  witli  by  sym- 
bol. Then  the  mati,  having  become  hermaphrodite,  half 
male,  half  female — i.  e.,  half  ♦,  and  h^Xi  Jish,  or  mm,  or 
hovah,  mn — came  up  out  of  the  water  (type  of  the  resur- 
rection), and  immediately  the  Holy  Spirit  descended  on 
him  in  the  for7n  of  a  dove;  which  is  simply  a  final  deter- 
minative indexing  the  perfecting  of  the  ritual  or  S3^mboli- 
zalion.  A  voice  is  heard  :  "  This  is  my  beloved  son."  He 
was  now  become  the  son  of  both  Elohim  and  Je-hovah  ; 
he  was  both  diameter  and  circumference.  His  head  was 
Rash,  or  213-0  =  355  X  6  ;  and  as  he  "  was  about  30  years 
{shanahs,  355)  of  age"  (Matthew,  16),  then  71  X  30  = 
2130:  or  the  dove,  71,  coming  down  on  h.\s  head,  multi- 
plied by  his  shanahs,  or  years,  equaled  71  X  30=  2130, 
or  the  head,  or  beginning  of  creation  in  the  first  word  of 
first  Genesis.  He  was  called  sofi  of  man,  after  the  words 
of  Daniel  the  prophet.  This  word  is  taken  by  Daniel  from 
the  26th  verse  of  4th  Genesis:  "And  to  Seth  (Hi^*,  the 
year,  '  on  coins,  and  in  Phenician  HJC^,  Hu ,'  Fuerst, 
under  n^C^*),  was  born  a  son,  whose  name  he  called  Enosh," 
or  Ben  Enosh.  This  Enosh  was  the  "  Son  of  utan^''  and 
placing  the  values  of  the  letters  as  the  word  runs,  one  gets 
the  meaning  of  the  solar  year,  365,  and  the  luni-solar  year 
indirectly,  or  by  implication  ;  for  the  word  is  C^"lJ3"J<)  and 

365-1=364, 


226  Appendix  III.  §  91. 

which  last  is  the  woman  year  of  52  X  7  =  364.     And,  in- 
deed, Scth,  nC^,  implies  this  form  of  use  for  3-1-4  =  7. 

JVote  as  to  Fishes. 

The  symbol  of  the  ^'■Jisk'^  was  a  favorite  one  among  all 
the  ancients.  Mr.  Bryant  shows  its  origin,  in  the  mythol- 
ogies, to  have  been  in  the  figure  of  the  Deluge  ;  the  type 
being  of  a  fish  with  the  head  of  a  man.  In  Phenicia, 
especially,  it  was  of  great  import  in  the  idol  Dagon. 
The  Christian  Kabbala,  or  Gnosticism,  deals  very  largely 
in  the  mention  of  fishes ;  in  such  sort,  that  it  may  be  said 
to  be  rested  upon  the  symbol,  though  its  use  ever}' where  is 
made  to  appear  as  incidental  and  natural.  The  New  Tes- 
tament narratives  have  been  so  highly  colored  by  the  kab- 
balistic  import,  that,  commonly,  too  sweeping  or  embracing 
a  quality  has  been  given  to  the  idea  of  fishermen,  as  ap- 
plied to  the  apostles.  The  character  of  Jishertncn,  it  is 
true,  is  attached  to  Peter  and  Andrew,  to  John  and  James  ; 
but,  beyond  the  little  that  is  said  of  their  catching  fish  with 
nets  in  boats,  no  great  stress  is  laid  on  jishing  as  a  trade, 
or  fixed  occupation.  There  was  sufficient  to  introduce  the 
use  of  the  ancient  symbol,  without  departing  from  what 
might  truthfully  have  been  the  case  as  to  fishing  in  the 
Jordan.  The  fishing,  as  conducted  by  these  men,  was 
in  the  sea  of  Galilee,  or  of  Tiberias.  This  lake,  or  sea,  is 
but  an  enlargement  of  the  river  Jordan,  where  it  spreads 
out  into  wide  water,  or  small  lake,  or  rather  pond,  of  some 
ten  to  twelve  miles  in  length  by  about  six  miles  in  breadth. 
The  fishing  carried  on  in  it  was  in  ships,  or  small  fishing 
vessels,  with  sails,  by  means  of  seines  or  nets.  The  popu- 
lation to  be  supplied  was  a  dense  one  at  that  time,  and  the 
occupation  is  represented  as  pertaining  to  quite  a  class, 
thus  exhibiting  a  settled  business.  It  seems  impossible 
that  this  could  have  been  the  case.  The  only  condition  by 
which  fishing  of  that  kind  could  have  existed,  and  could 
have  been  carried  on  as  a  trade,  in  such  a  piece  of  water, 
would  have  had  to  depend  upon  a  constant  supply  of 
fish  to  catch,  from  some  large  body  of  water  as  a  breeding- 


§  gi.  Appendix  III.  227 

ground,  the  fishing  taking  place  in  what  is  called  the  rtiJi 
of  the  fish,  at  stated  seasons.     Communication  with  such  a 
body  of  water — as,  for  instance,  the  ocean — would  stock  such 
a  pond  with  a  few  fish  at  all  times,  but  not  in  such  quantity 
as  to  justify  an  occupation   as   described,  save  at  certain 
seasons  of  the  year.     This  is  a   simple  and  truthful  state- 
ment, justified  by  all  the  registered  experience  in  such  mat- 
ters.    But  the  conditions  of  the  Jordan  river  are  fearful  for 
sustaining  fleets  of  fishing  vessels  plying  the  trade  on  the 
waters  of  the  sea,  or  pond,  of  Tiberias.     It  is  almost  a 
straight  stream,  with  a  very  rapid  descent  from  its  source 
to  its  mouth  (it  is  called  The  Descender)-,  save  when  it  en- 
larores  out  in  the  morass  of  Merom  and  into  the  waters  of 
this  inland  sea.     Its  condition  parts  of  the  year  is  that  of  a 
brook.     It  rises  in  the  springs  of  Mount  Hermon,  and, 
after  a  run  down  hill  of  150  miles,  empties  into  the   as- 
phaltum  lake,  in  which  no  fish  can  live  or  breed.     If  the 
country  was  far  enough  north,  brook  trout  might  abound  to 
some  extent  in  its  waters  ;  but  these  would  have  to  be  pre- 
served with  care,  for  it  would  require  but  little  angling  to 
depopulate  it  of  this  species.     The  whole  of  the  fisheries 
of  the  Sea   of  Galilee  would,  therefore,   have  to  depend 
upon  its  own  breeding-grounds,  of  which,  it  may  be  said, 
there  can  be  none,  save  of  the  species  of  what  are  called 
mud  or  cat  fish,  which  were  prohibited  from  use,  as  having 
no  scales,  and  a  few  others,  utterly  unfit  to  found  a  fisher}^  on, 
as  a  business  of  continuous  calling.     The  conclusion  seems 
irresistible,  that  to  have  supported  a  mode  of  fishing,  such 
as  commonly  thought  and  taken   to  have  been  the  case, 
would  have  required  a  continuous  miracle  of  keeping  up 
the  supply. 

iMl  this  seems  to  confirm  the  idea  that  the  relation  of 
fishing  was  to  raise  a  symbol,  comporting  with  and  neces- 
sary to  display  ancient  uses  and  meanings. 


228  Appendix  IV.  §  92. 


APPENDIX   IV. 

A  Method  of  Construction  of  the  fulian  Calendar^  from 
the  Different  Tear  Values  of  the  Aneients. 

§  92.  (ff.)  An  advanced  step  can  now  be  taken,  even  to 
a  way  of  the  construction  of  the  Julian  calendar,  from  means 
obtained  from  the  Garden  of  Eden  data.  By  7V"<3r>^,  the 
Garden  of  Eden  was  one  of  the  birth  of  time  and  of  man. 
Nork  was  right,  and  his  conjecture  is  supported  by  the  hid- 
den reading  in  the  description  of  this  garden.  It  is  shown 
elsewhere  that  one  numerical  form  for  this  garden  was  for 
the  production  of  the  -woman  from  man^  or  5315  from  113. 
The  woman  having  been  thus  formed,  from  her,  again,  as 
a  source  of  generation,  the  production  of  man  commenced. 
But  it  has  been  seen  that  113  is  diameter  to  a  circumfer- 
ence of  355  ;  and  that  355  is  converted  into  73i  year  measure 
under  its  value  in  the  Hebrew  word  skanah,  year,  while, 
also,  1130-I-  is  a  circumference  to  a  diameter  of  360,  which 
was  the  standard  year.  So,  while  one  phase  of  the  garden 
glyph  is  given  up  to  the  production  of  humanity,  under  an- 
other phase,  by  another  numerical  system,  there  is  shown 
a  springing  of  time  measures.  The  two  phases  touch  each 
other  in  a  numerical  link.  The  full  form,  as  already 
given,  is 

355  ^  360  r  365 

I     >  I  J    I 

354  ^  359  ^  364 ; 

where,  from  355,  365,  the  first  being  the  Hebrew  shanah, 

or  year  word  of  355,  and  the  second  the  solar  vague  year, 

by  a  reduction  of  one,  there  is  obtained  the  ancient  lunar 

year  of  354,  and  the  luni-solar  year  of  364.     It  is  seen 

that,  through  the  value  355,  the  man  value,  and  through  it 

the  woman  value,  is  linked  on  to  a  system  of  time  measures. 

Now,  the  Garden  of  Eden,  under  another  phase,  is  but  the 


§  92-  Appendix  IV.  229 

use  of  the  number  7,  as  the  7th  day,  and  is,  in  the  disphiy 
of  this  use,  pictured  variously  by  the  different  ancient  na- 
tions. That  of  the  Hindus  is  the  most  clearly  marked,  as 
descriptive  of  the  Hebrew  intention.  The  picture  is  that 
of  tlie  woman  hermaphrodite,  Indrance-Indra,  the  nature 
goddess,  or  tlie  Issa  of  the  Hebrews,  which,  in  all  proba- 
bility, was  the  Isis  of  the  Egyptians,  seated  on  the  ground, 
the  top  of  a  tree,  which  springs  from  h-er  back  and  shoul- 
ders, spreading  over  her  head,  tlius  indicating  her  as  the 
connectinjT  link  between  the  measures  of  the  heavens  and 
of  the  earth  ;  the  top  of  the  tree  indicating  the  celestial 
circle  of  360°.  She  is  but  a  play  upon  the  values  113  :  355. 
But  passing  from  these  values  to  the  display  of  others :  In 
one  form  of  this  woman,  the  heel  of  the  left  foot  is  bent  for- 
ward, so  as  to  be  presented  to,  or  before,  the  mouth  of  the 
pudenda,  which  is  closed  by  bands,  distinctly  marked  as  7 
in  number.  Of  course,  this  location  is  significant  of  birth, 
and  here  the  basic  numerical  value  is  7,  thus  attaching  this 
as  the  holy  number  of  generation.  How  is  this  number, 
then,  connected  with  any  feminine  trait,  having  relation  to 
the  generation  of  man  and  of  ti7ne?  Very  simply.  7  is 
the  number  of  natural  days  in  the  week,  and  a  day  is  a 
natural  measure  of  time.  7  X  4  =  28  days,  the  time  period 
in  days  for  the  occurrence  of  the  menstrual  flow,  which  is 
indicative  of  periods  of  conception.  28  X  10=  280  days, 
is  the  period  indicative,  in  medical  jurisprudence,  of  the 
birth  of  man,  whose  value  is  113  diameter  to  a  circumfer- 
ence of  355,  as  shown.  28  X  13,  or  52X7,=  364  days, 
which  is  the  period  indicative  in  nature  of  the  birth  of  the 
3"ear.  The  number  7,  then,  as  at  the  base  of  these,  is  the 
holy  birth  number  factor.  The  method  of  deriving  the  year 
values  has  been  shown  as 

355  —  I  =  354  360  365  —  I  =  364, 

and  here  through  the  use  of  7,  the  mark  on  the  pudenda 
of  the  woman  (who  is  elsewhere  shown  to  be  derived  from 
the  ■jnat!  as  113  or  311  ;  and,  in  fact,  who  becomes  by  add- 
ing up  the  values  attached  to  her  name  311,  or  the  value 
of  the  man  again  in  this  number,  so  that  the  two  stand  face 


230  Appendix  IV.  §  92. 

to  face,  the  countermart  (ITJIJID)  ot"  each  other  as  311 — 113, 
yet  so  that  read  either  way,  and  the  one  is  the  other,  the 
hermaphrodite  idea  again  cropping  out),  is  seen  to  spring 
the  time' value  364,  which  thus  is  shown  to  be  a  connecting 
link,  worked  up  to,  through  the  methods  of  use.  In  other 
words,  there  is  shown  to  be  a  correlation  between  the  birth 
of  man  and  the  birth  of  time.  Such  being  the  case,  the 
circle  of  the  pudenda,  once  being  selected  as  correlating 
time  with  human  birth,  can  be  taken  as  symbolizing  any 
stage  or  condition  of  such  birth  :  either  it  may  be  28,  as  a 
mark  of  conception,  or  280,  a  mark  of  human  birth  ;  or  taking 
the  result  for  the  process,  it  may  be  taken  as  113,  man,  this 
as  a  diameter  value  implying  its  circumference  of  355, 
and  also  the  scale  of  time  measures  355,  360,  and  365, 
proceeding  from  it;  or,  again,  as  364,  a  year  time  value; 
and  so  on,  agreeably  to  any  connecting  value.  Anciently, 
this  same  idea  was  displayed,  by  implication,  in  the  Egypt- 
ian astronomical  charts  of  the  28  lunar  mansions,  as  the 
birtli  circle  of  time.  This  subdivided  for  the  28,  into  13 
each,  would  indicate  the  364;  and  this  last  would  be  rep- 
resented by  a  seJrpent  of  365,  bent  into  a  circle  and  swal- 
lowing one  unit  ojf  its  length.  In  Hebrew,  both  serpent 
and  brass,  for  another  meaning,  had  that  of  the  female 
pudenda ;  but  the  serpent  had  the  hieroglyph  of  the 
letter  13,  or  9,  which  is  also  the  base  of  6561,  the  Parker 
form. 

(The  mouth  of  the  pudenda,  as  signifying  tjie  place  of 
birth,  or  source  of  all  things,  is  also  significant  of  another 
striking  feature,  in  this,  that,  as  virgin,  no  conception,  and 
therefore  no  birth,  can  take  place  without,  first,  the  shedding 
of  blood.  This  perhaps  may  have  been  the  source  of  doc- 
trinal teaching,  as  aflx)rding  a  type  of  the  spiritual  birth,  in 
the  plirase  that  "  ruithoitt  the  shedding  of  blood  there  can 
be  no  remission  o_f  sins,'" — i.  e.,  no  birth  unto  righteousness. 
The  very  word  siti,  in  the  Garden  of  Eden  scene,  conveys 
the  idea  of  sexual  intercourse,  and  this  idea  is  held  to  mod- 
ernly,  in  the  phrase  "INIarie  conyue  sans  peche."     Of  this 


§  92.  Appendix  IV.  231 

intendment,  circumcision,  or  the  bloody  circle,  was  but  a 

Advancing  from  the  source  to  the  development  of  divis- 
ions of  the  year,  if  the  forms 

365  ^  r  355 

^  360  j 

364  ^  ^  354 

are  taken  as  measures  of  year  time,  where  the  year  value 

of  365  is  based  on  another  of  360  days,  of  12  months,  of 
30  days  each,  with  the  intercalary  number  of  5  days,  with 
the  other  forms  arising  from  the  number  7,  as  indicating 
the  woman  use,  from  these  there  can  be  derived,  it  is 
thought,  a  scheme  for  the  construction  of  the  Julian  cal- 
endar. 

(i.)  One  style  of  year  is  that  of  364  days,  based  upon 
the  menstrual  month  of  28  days,  as  follows  : 

28  X  13  =^364  days. 

(2.)  Another  style  is  that  of  360  days,  based  upon  the 
month  of  3a  days,  as  follows  : 

30  X  12=  360  days. 

(3.)  (2.)  was  taken  as  the  standard,  to  which,  at  the 
close  of  the  year,  5  days  were  to  be  added,  to  make  up  the 
full  solar  year  of 

365  days. 

(4.)  Therefore,  take  the  standard  at  12  months  of  360 
days,  of  which  one  month  had  to  be  the  characteristic  of 
the  style  under  (i.),  or  of  28  days.  Then  there  will  be  11 
(eleven)  other  months  of  30  days  each,  or  330  days,  with 
a  needed  surplus  of  2  days,  to  make  the  full  year  of  360 
days,  and  a  requirement  of  5  more  days  to  make  up  the 
solar  vague  year  of  365  days.  It  will  be  seen  that  the  sur- 
plus days  thus  needed,  are  in  number  7. 

(5 .)  Now,  to  make  combination  of  all  these  subdivisions, 
so  as  to  make  a  one  year  circle  of  365  days,  divided  into 
12  divisions,  or  months,  and  yet  so  as  to  indicate  the  pro- 
cess, proceed  to  the  distribution  of  these  7  days,  as  far  as 
possible,  among  the  months,  isolating  the  one  month  of  28 
days,  then  there  will  result : 


232  Appendix  IV.  §  92. 

(6.)     I  month  of  28  clays,  28  days. 
7  months  of  31   days,  217     " 
4  months  of  30  days,  left  as  a  resi- 
due over,  of  the  standard  year,  120    " 


Making  a  total  of  the  Julian  calendar  year,  365  " 
agreeably  to  its  known  divisions;  which,  in  fact,  was  the 
work  of  an  Egyptian,  and  which,  ancientl}-,  belonged  both 
to  the  Egyptians  and  Hebrews.  "  Macrobius  says  that 
Ceesar  was  indebted  to  Egypt  for  his  correction  of  the  cal- 
endar :  '  Nam  Julius  Cgesar  .  .  .  siderum  motus  .  .  . 
ab  vEgyptiis  disciplinis  hausit.'"  (Rawlinson's  Herodo- 
tus, note  6  to  Book  H,  chap.  51.)  See  also  Sharpe's 
Egypt*  Vol.  H,  p.  52. 

The  Possible  ^^HccP^  Meaning  of  the  217  Days. 

(5.)  The  word  heel,  of  which,  or  as  to  which,  the  real 
substance  is  placed  as  noted  in  the  Hindu  picture  of  the 
Garden  of  Eden,  is  also  of  very  great  moment  in  the  Hebrew 
glyphs.  It  is  the  name  Jacob  (Dpl^"%  or  yah-is  heel),  who 
notoriously,  in  his  children,  was  the  founder  of  the  year  of 
12  and  13  months.  (See  Nork,  Worterbuch,  under 
"Jacob.")  It  is  used  significantly,  among  others,  as  to 
these  very  relations,  in  the  garden  description,  in  the  phrase 
"  Thou  shall  cover  to  it  a  head,  and  it  shall  cover  to  thee  a 
heel."  It  is  seen  that  the  heel  is  placed  before,  as  touching 
the  mouth  of  the  pudenda.  In  the  above  scheme  for  the 
formation  of  the  calendar,  the  mouth  of  the  pudenda  is 
taken  as  the  woman  month  of  28  days.  Then  there  is 
taken  seven  months  of  30  days  each,  plus  the  distribution 
among  them  of  a  week  of  seven  da3's,  in  all  217  days.  In 
Hebrew,  the  word  heel  is  DpJ/,  okbv,  the  character  values 
running  with  the  word  being  712,  or,  in  the  reverse,  217  ;  so 
that  this  heel  standing  before  the  woman  month  of  28,  as  a 
foundation,  may  be  added  to  it,  as,  in  fact,  an  additional 
value  of  217  (or  712)  of  the  pudenda,  the  two  amounting 
to  28  -f  2171=  245  days.  For  another  style  of  calculation 
to  make  up  the  standard  year  of  360,  there  will  be  lacking 


§  92.  Appendix  IV.  233 

115  days  ;  the  360  being,  perhaps,  indicated  by  the  spread- 
ing tree  top  over  the  woman-man's  head,  indicating  rash^ 
or  213,  or,  as  the  number  113,  the  diameter  36  or  360. 
Then  28 -j- 217  +  115  =  360,  and  adding  the  epagomenai 
5,  the  year  value  becomes  365.  Thus  this  hccl^  or  217, 
seems,  by  change,  to  become  the  pudenda  itself,  with  28 
(and,  as  has  been  noted.  Dr.  Donaldson  ascribes  this  mean- 
ing to  the  word). 

This  leads  to  hazarding  a  suggestion  as  to  possible  deter- 
minative sentences  in  Genesis  as  to  this  purpose.  It  is 
stated  in  \h^  fourth  chapter  :  "And  she  conceived  and  bare 
Cain,  and  said,  I  have  measured  (otherwise,  gotten)  a 
man  (113),  even  Jehovah."  It  is  extraordinary  that,  in  the 
Hebrew,  the  word  Jehovah  is  here  in  affosition  with  the 
word  man,  there  being  no  such  reading,  by  possibility,  as 
'■''from  the  Lord.'"'  Man,  as  113-0,  is  circumference  to  a 
diameter  of  360 ;  and  fehovah,  for  one  of  its  symboliza- 
tions,  is  the  year.  Now,  the  pudenda,  or  woman,  having 
become  28  +  217  =  245,  it  requires  just  115  days  to  make 
up  the  full  complement  of  the  perfect  standard  year  of  360. 
Now,  she  says  as  to  Cain,  that  having  borne  him,  she  has 
measured  a  man,  or  a  circumference  to  a  diameter  of  360, 
even  the  perfect  year,  or  Jehovah ;  possibly  meaning  that 
she  had  produced  the  full  complement  to  make  up  that 
amount,  or,  in  other  words,  that  in  bearing  Cain,  the  full 
standard  year  was  completed  :  for  the  value  of  the  word 
Cain,  [♦p,  is,  as  the  letters  run,  115,  or  just  the  number 
required  to  make  this  complementary  number  good.  This 
view  is  strengthened  by  that  which  follows  consecutively 
on  this — viz.,  the  birth  of  Seth  (or  jlSi^,  the  year),  and  the 
birth  to  him  o{ Enosh.  It  is  stated  :  "And  to  Seth,  to  him 
also,  there  was  born  a  son  ;  and  he  called  his  name  Enosh: 
then  began  men  to  call  themselves  fehovah''  The  two 
passages  are,  beyond  doubt,  connected  together  for  an  oc- 
cult purpose,  by,  in  one,  the  term  '■'■  measuring  a  man  even 
fehovah;''  and,  in  the  other,  tlie  term  '■'■men  calling  them- 
selves fehovah:"  for  these  are  the  only  such  uses  of  tlie 
word  "Jehovah"  in  all  the  Bible.    Seth  being,  as  the  word 


234  Appendix  IV.  §  92. 

can  be  taken,  the  year  (Fuerst  under  il^^),  the  name  of  his 
son  Enosh,  or  CIJ'N,  gives  the  other  and  two  final  values 
of  the  year,  in  the  expression  of  the  values  of  the  letters, 
as  they  run — viz  : 

365  —  1 

C^IJ  -  N* ; 
where  there  is  the  full  vague  year,  with  the  unit  one,  by 
which    can    be   taken    the    form  365  —  i  =  364.     In  this 
special  connection,  the  word  Jehovah  must  be  taken  as  the 
glyph  of  the  perfect  year  circle  of  360. 

The  above   Use  somewhat  strengthened  by  the  Zodiacal 

Sign  of  the  Fishes. 

(c.)  Man  and  woman,  in  the  garden  scene,  being  but  a 
play  upon  the  value  113,  on  which  355  is  raised,  the  other 
scheme  connected  with  the  -pudenda  of  the  woman  is  but  a 
play  upon  the  use  of  this  number  as  a  foundation,  the  ram- 
ifications of  which  have  been  somewhat  set  forth.  The 
above  method  of  construction  of  the  Julian  calendar  is  in  a 
measure  clinched  as  rightly  taken,  when  the  character  sign, 
or  symbol  of  the  month  of  28  days,  or  the  menstrual 
month,  is  considered.  On  the  astronomical  charts,  the  sym- 
bol of  the  month  of  28  days  is  the  Jish.  In  the  glyph  of 
"Jonah  and  the  jish,  the  Hebrew  name  for  Jonah  is  also  that 
of  the  dove.  This  is  but  a  play  upon  the  ark  of  Noah  and 
the  dove.  Jonah  goes  into  the  fish's  belly,  and,  correla- 
tively,  the  dove  goes  into  the  ark.  In  the  description  of 
the  flood  picture,  the  word  dove  is  used  just  five  times.  The 
value  of  the  word  dove,  or  Jonah,  is  71,  and  5  times  this 
value  is  355,  or  the  circumference  value  under  considera- 
tion. Now,  five  times  the  value  of  the  man,  or  aish,  is 
113  X  5  =565.  The  word-for_/f5/z,  or  nun,  is  565,  also,  or 
in  fact,  the  multiple  of  113,  this  very  diameter  value.  In 
this  symbol  of  the  month  of  28  days,  the  reference  is  very 
salient,  as  the  astronomical  sign  of  this  month  in  the  ancient 
zodiac  was  that  of  two  fishes,  or  565  X  2  =  1130  ;  and,  as 
has  been  shown,  1130  +  is  circumference  to  a  value  of  360, 
the  value  taken  as  standard  for  the  year.     Then,  indeed, 


§  92-  Appendix  IV.  235 

the  sign  of  the  menstrual  month  of  28  days  is  360;  but 
this  month  is  based  on  the  pudenda  as  7,  and  as  a  time 
measure  this  is  also  the  heel,  or  217.  28  +  217  =  245,  and 
360  —  245  =  115,  or  Cain,  of  whom  the  woman  says  he  is 
the  measure  of  Jehovah  (or  even  Jehovah  himself),  which 
can  stand  for  the  year  circle.  Then  360  being  the  stand- 
ard, and  28  and  217  being  already  had,  to  make  the  full 
vague  year  requires  120  days,  or  just  4  months  of  30  days 
each,  so  that  28  -f-  217  (=  31  X  7)  -f-  120  (=  30  X  4)  =  365, 
the  Julian  year  in  its  known  divisions. 

The  xuord  Paradise,  as  having  a  Bearing  on  this  Subject. 
Another  confirmation  of  the  time  birth  use  of  the  Garden 
of  Eden  is  to  be  found  from  kabbalistic  sources,  in  the 
meaning  of  the  term  Paradise.  This  word,  so  far  as  com- 
mented on,  has  no  meaning,  and  is  supposed  to  be  derived 
from  a  foreign  source.  By  Fuerst,  it  is  a  word  used  for 
metaphysical  purposes,  or  for  mystic  uses.  It  is  a  word  for 
which  the  reputed  authority  of  the  Savior  is  given  as  being 
correctly  used  for  the  heavenly  Garden.  It  is  the  word 
used  for  the  Garden  of  Eden  by  the  Seventy.  The  mean- 
ing of  the  term  is  a  very  simple  one.  It  is  a  Hebrew  com- 
pound of  the  verbal  Par  ad,  115,  to  divide,  and  the  ap- 
pended letter  samech,  D,  signifying  the  circle  bounded  by 
one  side  of  a  square.  The  letter  5a;;zfc/z  stands  for  60,  and 
the  face  of  a  square  being  60,  the  full  cube  (to  represent  the 
full  sphere)  having  6  faces,  would  represent  60  X  6  =  360; 
so  that  the  term  Pardess,  or  Paradise,  would  signify  the 
division  of  the  circle  of  360.  In  fact,  Kabbalism  takes  the 
samech  as  the  divided  circle,  which  the  Hebrews  repre- 
sented in  -plane  forms,  as  of  the  square  for  circle,  and  as 
of  the  cube  for  sphere.  Taking  the  Garden  of  Eden,  under 
this  Paradise  use  of  360,  then  it  becomes  the  year  value 
of  360  days  of  12  months,  of  30  days  each,  as  a  standard 
on  which  to  construct  the  changes  mentioned  through  the 
man-woman.      So,  also,  60  designates  the  height  of  the 

king's  chamber  in  the  pyramid,  as  also — its  base  side. 


236  Appendix  IV.  §  92. 

The  Heel  Vahie,  aff  caring  as  Connected  with  the  Meas- 
ures of  the  ^lecn^s  Chamber. 

{d.)  Heel  is,  as  said,  712,  the  reverse  use  of  217  having 
been  used  above.  Making  use  of  the  value  as  712,  it 
adapts  itself  directly  with  the  pyramid  measures  in  the 
queen's  chamber,  for 

56.5  :  177.5  :  :  72  :  226.1946  ::  226.63  :  712; 
or  712  is  thus  exhibited  as  a  circumference  to  a  diameter  of 
226.63,  which  is  the  length  of  one  of  the  sides  of  the 
queen's  chamber  in  this  pyramid.  It  is  a  very  curious 
circumstance  that  the  length  of  the  opposite  side  of  this 
room  is  given  at  227.-I-J  and,  in  fact,  the  Hebrew  word  for 
mcnihrum  virile  is  ^3t,  or,  reading  its  values  in  the  reverse, 
227.  It  is  very  curious  also  that  217  {heel)  X  3  =651,  or, 
numerically,  recurrence  of  the  Phoenix  time  period,  marked 
by  the  crossing  of  the  disc  of  the  sun  by  the  planet  Mer- 
cury ;  as  also,  by  Parker,  the  complete  travel  of  the  mag- 
netic pole  about  the  earth. 

{ei)  How  strange  it  is  that,  whether  the  keys  of  these 
matters,  as  connected  with  the  Garden,  are  taken  from  the 
narrative,  or  from  numbers,  or  from  the  elemental  geomet- 
rical elements,  the  phallic  use  is  always  to  be  found  as  the 
underlying  one.  The  Parker  forms  rest  on  the  relation 
(transcendental)  of  the  equilateral  triangle,  and  of  the 
circle,  as  being  at  the  opposite  extremes  of  nature  ;  and  so, 
because  the  former  is  measurable,  the  latter  through  it 
can  be  made  measurable.  The  measure  itself  becomes 
manifest  in  terms  of  the  square.  Now,  by  Kabbala,  of  the 
interlaced  triangles,  the  one  with  the  point  down  is  female. 
So  is  the  circle.  The  pointed  obeliscal  shaft  was  squared, 
and  was  universally  looked  on  as  phallic.  The  uses  then 
carry  these  emblems  as  the  enunciations  of  the  uses  of 
these  geometrical  forms.  It  is  the  phallus  which  is  the 
vehicle  of  enunciation  ;  and  truly  enough,  as  the  sacr,  or 
carrier  of  the  germ,  its  use  passed  down  through  ages  to 
the  sacr-factuni  of  the  Roman  priest,  and  the  sacr-fice  and 
sacr-7uent  of  the  English-speaking   race.     It  is  perfectly 


§  92.  Appendix  IV.  237 

true  that,  anciently,  even  with  the  Hebrews,  the  highest 
religious  or  spiritual  types  were  (to  us  grossly)  sexual. 
The  Christian  type  of  a  spiritual  birth  was,  by  the  rite  of 
baptism,  a  wonderful  refinement,  while  the  symbol  of  the 
same  means  of  birth.  But  more  anciently,  the  same  type 
was,  by  circumcision,  a  right  performed  on  the  sacr.  It, 
too,  symbolized  a  birth,  or  rather  marriage,  indicative  of 
birth.  The  great  symbol  was  in  the  shedding  of  the  blood 
of  separation,  and  yet  of  union,  typifying  generation  by 
marriage. 

As  this  is  descriptive  of  a  simple  fact  of  ritualism,  its 
force,  as  casting  light  on  what  has  been  said  as  to  marriage 
conversation,  is  manifest.  A  wonderful  illustration  of  the 
underlying  meanings  of  the  rite,  as  sexual,  can  be  offered. 
When  the  sons  of  Jacob  offer  conditions  to  the  Scheche- 
mites,  they  say  (Gen.  xxxiv.  14)  :  "  Der  eine  vorhaut  hat, 
denn  eine  schmach  wiire  das  fiir  uns,"  which  is  a  better, 
because  more  literal,  translation  than  the  English.  But 
the  word  schmach,  in  the  English,  "for  that  {were)  a  re- 
■proach  to  us,"  is  not  a  literal,  nor  is  it  a  good  translation. 
The  Hebrew  word  is  HS'irT,  charaphah,  which  is  translated 
schmach  and  reproach.  The  primary  and  real  meamng 
of  the  word  is  "  (i.)  prop,  jissiire,  split,  therefore  ragina, 
female  pudenda.''^  (Fuerst.)  The  proper  translation  is : 
For  he — "  who  has  a  prepuce, — that  (or  the  prepuce,  >?in) 

is  a  mark  of  a  vagina  to  us  ("l^/rTfi^lfT'^)."  In  other  words, 
and  in  short :  He  who  has  the  prepuce,  is  a  woman  to  us. 
This  idea  is  continued  to  modern  times,  for  Lane  (at  the 
time  of  his  translating  the  Thousand  and  One  Nights)  no- 
tices, in  a  note,  as  to  the  preparations  for  the  performance 
of  the  rite  of  circumcision  of  j^outh,  that,  up  to  the  time  of 
the  ceremony,  they  are  paraded  around,  dressed  in  girls' 
clothes,  or,  to  use  his  expression,  m  feminine  attire.  The 
type  of  the  spiritual  rebirth,  by  circumcision,  was  the 
shedding  of  blood  in  the  consummation  of  the  marriage 
rite.  This  view  is  fully  enforced.  Under  |nn,  chathan, 
Fuerst  says  : 

"  Properly,  one  allied,  married  ;  hence  (i.)  at  a  marriage  feast, 


238  Appendix  IV.  §  92. 

a  bridejo^room,  who  rejoices  in  conducting  home  the  bride,  Is. 

62,  5,  and,  like  the  latter,  exults  in  that  day  (see  H/D),  jfef-  7' 
34;  16,  9;  25,  10;  who  wears  a  chaplet,  So7ig-  of  Sol.  3,  11, 
and  encircles  his  head  like  a  priest,  Is.  61,  10  ;  who,  with  joyful 
spirit,  and  full  of  life's  enjoyment,  goes  forth  from  the  bride- 
chamber  (Hijn^irT)  with  the  feeling  of  vigor,  yo.  2,  16;  Ps. 
1.9,  6  ;  after  he  has  become,  in  the  wedding  night,  by  the  offering 
of  the  maiden's  blood,  a  D\t3T  jiini  chathan  damim — i.  e.,  one 
allied  by  the  maiden's  blood  {Ex.  4,  25,  26),  an  idea  which  was 
subsequently  transferred  to  circumcision.  (2.)  A  bridegroojn 
of  circumcision — i.  e.,  who  is  allied  to  God  by  the  dedication  of 
the  blood  of  circumcision,  called  from  the  consummation  of 
marriage.^'' 


§  93-  Appendix  V.  239 


APPENDIX  V. 

The  Flood    and   the  Ark  of  Noah,  with   their  strange 
Kabbalistic  Biblical  Relations. 

§  93.  It  must  be  borne  in  mind  that  the  substance  of  the 
Old  Testament  lays  in  the  books  of  the  Lazu.  All  the  re- 
mainder is  but  expansion,  explanation,  targums,  enforce- 
ments, etc.  The  Law  is  divided  into  the  framing  of  the 
ritual,  and  the  enunciation  of  moral  precepts,  as  the  cor- 
related enforcements  of  the  law  in  the  workings  of  the  souls 
of  men.  There  is  far  more  space  taken  up  in  the  estab- 
lishment of  the  ritual  than  in  the  inculcation  of  the  moral 
precepts.  The  ritual  properly  rests  upon  the  construction 
of  the  great  pyramid,  with  its  contained  measures.  The 
building  of  the  pyramid  in  the  books  of  the  Law  occupies 
all  the  first  chapters  of  Genesis,  to  the  construction  of  the 
ark  of  Noah.  The  determinatives  marking  the  completion 
of  the  pyramid  structure  are  very  marked,  and  are  con- 
tained in  very  brief  compass.  The  Parker  and  Metius 
measures,  in  the  queen's  chamber  especially,  and  elsewhere 
in  the  pyramid,  unfold  the  Jehovah,  or,  more  properly,  the 
Mosaic  or  Pharoah  measures  of  113  to  355.  It  would 
seem,  then,  that  the  queen's  chamber  answers  to  a  special 
part  of  the  Biblical  Garden  of  Eden. 

The  Biblical  Containment  of  the  Pyramid  Structure. 

(a.)  It  has  been  shown  how  the  numerical  formulations, 
on  which  the  pyramid  is  to  be  constructed,  are  to  be  found 
in  the  hieroglyphic  construction  of  the  Garden  of  Eden. 
Leaving  out  that  which  intervenes  as  having  no  recog- 
nizable key  of  solution,  the  determinatives  marking  the 
completion  of  the  -pyramid  as  to  its  mass,  are,  as  above 
stated,  very  marked  and  strongly  outlined. 


240  Appendix  V.  §  93- 

From  Adam  to  the  jlood  embraced  an  interval  of  1656 
years  (or  shanahs,  or  355's).  It  is  most  likely  that  these 
numbers  had  a  use,  just  as  they  read  in  value  ;  but  there  was 
another  and  kabbalistic  use  of,  on  occasion,  reading  a  value 
backward^  or,  for  1656,  reading,  as  the  more  occult  and 
more  exact  meaning,  6561,  and  this  is  the  Parker  square, 
the  source  of  the  enlarged  measures  of  the  pyramid  of 
Egypt,  as  has  been  fully  shown.  Such  a  use,  were  it  in- 
tended, should  be  accompanied  by  other  dcterminaiive 
marks  of  the  correctness  of  its  being  thus  taken.  In  this 
instance,  these  are  abundant  enough,  and  salient  enough, 
and  far-reaching  enough.     Some  of  them  may  be  given. 

The  use  of  the  names  Shem,  Ham^  and  yaphet,  as  De- 
terminative  of  Pyramid  Measures^  in  connection  with 
the  600  Tear  Period  of  iVoah,  and  the  500  Year  Period 
to  Shem,  Ham,  and  faphet. 

{b.)  Noah,  or  the  Stop,  or  £!nd,  or  Pest,  was  600  years 
of  age  at  the  time  of  the  flood  (years,  shanahs,  355  X  600  = 
213,  Push).  6561  is  the  source  of  the  enlarged  values  of 
the  pyramid  as  seen.  Now,  600  is  just  the  circumference 
to  the    height  of  the   king's   chamber  multiplied    by  10, 

or  190.985 +  ,  or  to  the — the  base  side  of  the  pyramid  as 

190.985+  feet;  and  the  variation  on  this,  or  190.237-}-, 
raised  from  feet  to  inches,  and  multiplied  by  4^^  to  equal 
the  variation  on  the  entire  circumference  of  the  pyramid, 
equals  the  true  solar  year ;  while  the  correlations  of  this 
value  give  the  earth's  diameter  in  miles.  So  also  this  600 
is  the  period  of  Divine  incarnation,  by  the  conjunction  of 
the  sun  and  moon,  as  by  Cassini : — that  measure  of  which 
Christ  was  the  foundation,  in  318,  and  the  measure  of 
transfer  onto  the  celestial  circle  of  360°,  in  the  number  608. 
But  this  period  of  600  years  is  signalized  by  another  of 
very  great  value — viz:  "Noah  was  (500)  five  hundred 
years  old,  and  Noah  begat  Shem,  Ham,  and  fafhet." 
(Years,  shanahs,  355  X  5  =i775-)  This  is  a  great  deter- 
minative sentence.     The  number  five  (5)  is  the  jl,  or  the 


§  93*  Appendix  V.  241 

womb,  or  fructifying  number  ;  for  the  rabbins  have  a  say- 
ing that  God  made  all  things  out  of  the  letter  il.  Two  of 
these  fives  in  the  center  of  the  Garden  were  equal  to  the 
numerical  value  10,  which  is  the  perfect  one,  or  yah,  which 
is  the  number  of  the  holy  of  holies,  in  its  divisions  by  the 
cherubims,  and  which  is  a  circumference  to  the  Christ 
value  of  318.  The  pyramid  thus  shadowed  forth,  in  its 
familiar  number  measures,  is  now  strongly  lined  out,  be- 
yond all  mistake,  by  use  of  the  power  (or  number  values) 
of  the  expression  of  the  three  names  of  the  sentence — viz., 
'■'•Shem  Ham,  and  yaphcti"     The  Hebrew  expression  is — 

(I.)      □  t:' 

D         rr 

n    £)        1 

Give  the  character  values  to  correspond  with  this  position  : 

(2.)       4  3 

4  8 

I 
48  6 

And  let  these  values  be  read  as  they  stand,  thus  :  444  is  the 
numerical  value  of  the  side  of  the  base  of  the  pyramid,  in 
cubits  {or  cherubims  ^222 -{- 222  =. /\i\^  ;  381  is,  in  feet, 
the  half  base  side  of  the  pyramid  ;  and  486  is,  in  feet,  the 
height  of  the  pyramid  : — all  in  the  standard  measures  of  the 
same,  as  coming  from  the  original  Parker  elements,  which, 
in  the  construction  of  the  Garden  of  Eden,  have  been  seen 
to  be  shadowed  forth,  by  the  use  of  the  Metius  values  of 
^^3  •  355-  And  so,  the  work  completed,  or  the  pyrapnid 
mass  outlined,  it  was  the  completion  of  the  grand  Stop, 
or  Rest,  or  Noah;  a  condition  which,  by  Bryant,  was  the 
origin  of  all  mythology. 

Method  of  Calendar  Correction   contained  in  the  Flood 

Narrative. 
But  while  the  means  were  occultly  being  laid  for  the 
exact  determination  of  cosmical  phenomena,  such  as  astro- 
nomical times  and  earth  measures,  agreeably  to  the  Parker 
method,  to  co-ordinate,  it  would  seem  also  that  the  narra- 


242  Appendix  V.  §  93. 

live  contains  other  methods  more  popular,  though  less 
exact.  The  description  of  ihe  Jlood  seems  to  contain  cu- 
rious methods  for  the  correction  of  time  periods,  and  the 
fastening  them  to  the  earth. 

Correction  of  the  600  Tear  Period. 

{c.)  One  of  the  commonest  methods  for  the  computation 
of  time  was  by.  taking  the  number  of  degrees  of  the  celes- 
tial circle,  for  the  number  of  days  in  the  year — viz.,  360 
degrees  were  made  to  stand  for  360  days.  Correction  was 
made  by  the  addition  of  5  days,  called  cpagomenai 
{iTzaybfjiZvax  ■fjfiipac').  Thus,  counting  to  the  end  of  the  ce- 
lestial circle  of  360  degrees,  for  360  days,  there  was  made 
a  stop,  or  rest,  or  Noah,  and  five  days  were  allowed  to 
pass  by  without  count.  As  the  day  was  marked  by  the 
rising  and  setting  of  the  sun,  the  giver  of  light,  and  the 
circle  of  the  day,  the  process  was  symbolized  by,  as  it  were, 
placing  five  days  in  a  box  or  ark,  thus  consigning  them  to 
oblivion,  by  blotting  out  the  light,  or  letting  the  day  pass 
without  count.  It  was  the  necessary  step  to  the  rebirth  of 
the  year.  The  process  was  that  of  setting  a  watch  by  the 
sun.  If  the  watch  has  gained,  say,  five  minutes  on  the 
sun,  correction  will  be  made  by  stopping  the  watch  for 
five  minutes,  and  then  starting  it  again.  The  similitude 
between  the  watch  and  the  sun  lays  in  the  connection  of 
the  passage  of  the  sun  through  the  signs,  as  it  has  relation 
to  the  seasons;  that  is,  from  year  to  year,  the  sun's  place 
in  the  signs  should  be  accompanied  by  a  corresponding 
condition  of  the  seasons,  whatever  that  might  be,  as  spring, 
summer,  autumn,  or  winter.  If  there  is  a  constantly  re- 
curring need  of  correction,  the  quantity  should  be  known, 
so  that,  being  made  at  the  appropriate  time,  the  coalescence 
between  the  sun  in  his  signs,  and  the  proper  season,  should 
always  be  maintained. 

It  is  very  evident  that,  prior  to  the  time  of  the  flood,  as 
narrated,  the  365  day  value  of  the  year  was  known  ;  and 
it  may  be  taken  that  the  correction,  by  means  of  the  epa- 
gomenai,  was  in  use.     The  relation  of  the  365  day  period 


§  93*  Appendix  V.  243 

to  the  364,  or  luni-solar  year,  seems  to  be  pointed  at  in  the 
name  Enosh,  or  365  —  i,  as  seen,  especially  as  the  name 
niy  may  be  taken  as  i/ie  year.  Also,  by  Philo,  Enoch, 
son  of  Jared,  was  the  father  of  the  solar  year,  marked  by 
the  365  years  of  his  life.  The  period  of  the  flood  seems 
to  mark  the  Stof,  or  JVoak,  for  a  greater  correction.  If 
the  correction  of  5  days  in  the  year  be  followed  some  length 
of  time,  it  will  be  found  that  the  seasons  will  begin  to  fall 

back — of  a  day  a  year,  or  a  whole  sign   in    120  years. 

Now,  the  celestial  sphere,  with  the  earth,  was  divided  into 
12  compartments,  and  these  compartments  were  esteemed 
as  sexcd;  the  lords,  or  husbands,  being,  respectively,  the 
planets  presiding  over  them.  This  being  the  settled 
scheme,  want  of  proper  correction  would  bring  it  to  pass, 
after  a  time,  that  error  and  confusion  would  ensue,  by  the 
comparttnents  coming  under  the  lordship  of  the  wrong 
planets.  Instead  of  lawful  wedlock,  there  would  be  illegal 
intercourse,  as  between  the  planets,  *^  sons  of  Elohhn,^''  and 
these  compartments,  "daughters  of  H-Adam,"  or  of  the 
€arth-xx\2iW  ;  and,  in  fact,  the  4th  verse  of  6th  Genesis  will 
bear  this  interpretation  for  the  usual  one — viz:  "In  the 
same  days,  or  periods,  there  were  untimely  births  in  the 
earth  ;  and  also  behind  that,  when  the  sons  of  Elohim  came 
to  the  daughters  of  H-Adam,  they  begat  to  them  the  off'- 
spring  of  harlotry,"  etc.,  astronomically  indicating  this 
confusion.  Such  being  taken  to  be  one  of  the  objects  of 
the  glyph,  the  astronomical  period  taken  is  that  of  the 
Stop,  or  JVoah,  which  was  600  years.  How  many  days 
would  have  to  be  put  in  a  box,  or  ark,  as  consigned  to  ob- 
livion in  count,  to  work  the  correction  of  this  period  ;  so  that 
the  seasons,  now  in  confusion  with  respect  to  the  planets,  or 
signs,  lording  over  them,  would  come  back  to  their  proper 
places  in  the  original  scheme,  or  every  woman  come  back 
to  her  proper  lord?  Or,  how  long  should  the  watch  be 
stopped  before  starting  again,  at  the  corrected  period? 
The  number  of  years  being  600,  the  period  of  confusion, 


244  Appendix  V.  §  93* 

or  error,   at  —  of  one  day  a   year,   would  for  this  time 

amount  to 

150 
days,  as  the  amount  of  the  Stop^  or  Rcst^  or  Noah.    Truly 

enough,  this  was  just  the  length  of  duration  of  the  flood 
over  the  compartments  of  the  earth,  wiping  off  the  old 
marks,  and  again  setting  the  seasons  right  with  the  stations 
of  the  sun.  The  idea  conveyed  by  the  termination  of  the 
flood  was  that  the  scheme  for  the  correction  of  the  600  year 
cycle  was  perfected  ;  and  the  whole  is  contained  in  the 
closing  verse  of  the  8th  chapter,  which  is,  as  it  were,  a 
general  determinative  of  the  process,  use  of  the  same,  and 
the  result.  The  Lord,  or  Jehovah,  says,  as  it  can  be  read  : 
"Circling,  winding,  or  turning  in  circles,  all  the  days  or 
periods  of  time  of  the  earth — viz.,  seed  time  and  harvest^ 
and  cold  and  heat.,  and  siunnier  and  whiter,  and  day  and 
night,  they  shall  not  be  separated  from  the  aecomflished 
condition  of  correction."  They  should  not  cease  to  be  in 
their  proper  and  appropriate  places,  with  irelalion  to  the 
sun.  Before  this,  by  error,  the  seasons,  by  name,  had  be- 
come inappropriate  to,  or  incongruous  with  their  meanings  ; 
but  now,  harvest,  by  name,  should  apply  to  the  actual 
season  of  harvest ;  summer,  to  the  actual  season  of  summer, 
and  so  on,  without  further  change  or  alteration,  for  the 
proper  amount  of  correction  and  its  use  was  now  known. 

The  fixing  a  Limit  for  the  Closing  and  Opening  of  the 
Year  at  the  Winter  Solstice  Point,  by  the  Figure  of  the 
Subsidence  of  the  Flood  and  the  Grounding  of  the  Ark. 

(d.)  But  while  a  cycle  correction  for  600  years  was 
thus  made,  it  seems  to  have  been  upon  such  grounds  as  to 
admit  of  accommodation  to  a  fixed  point  or  location  in  the 
circle  of  the  simple  year.  Bearing  in  mind  the  method  of 
correction  of  the  365  dav  year  on  that  of  360  days,  by 
means  of  the  epagomenai,  or  the  putting  of  5  days  in  a 
box,  a  scheme  can  be  suggested  as  of  ancient  use  of  deter- 


§  93-  Appendix  V.  245 

mining  such  a  point  and  location  at  the  winter  solstice.  In 
the  form 

355  360  365 

360  being  the  mean  between  355,  the  abstract  circumfer- 
ence value  (connecting  the  year  calendar  forms  with  the 
Garden  of  Eden  and  the  pyramid  forms  of  113  :  355  and 
20612  :  6561)  and  the  solar  year  value  of  365,  because  of 
this,  seems  to  have  been  used  as  a  standard  of  measure  of 
time.  The  equivalents  of  these  forms  are  to  be  found  in 
the  numbers  70,  71,  72,  and  73,  by  considering  them  as 
circles,  to  be  subdivided  in  five  units  for  each  unit  of  their 
vakies,  respectively,  as  70  X  5  =  35°'  7^  X  5=355, 
72  X  5  =  360,  and  73  X  5  =  365- 

{d.)  (i.)  Take  now  the  standard  measuring  circle  of 
360,  and  fasten  some  point  on  it  to  correct  the  year  time  to 
some  phenomenal  point  of  the  solar  year  proper,  say  the 
winter  solstice.  Then,  having  counted  360  days  to  this 
point,  the  five  epagomenai  days  are  put  in  a  box,  or  blotted 
out,  with  respect  to  this  measure  circle;  but,  on  the  other 
circle  of  365  days,  are  continued  on  to  make  the  full  solar 
year,  now  made  correct  with  the  seasons  to  a  definite  end 
or  stop  ;  from  whence,  after  the  lapse  of  four  years,  the 
bissextile  correction  of  one  day  can  be  made.  This  seems 
to  be  a  scheme  of  subordinate  showing  under  the  large  cor- 
rection of  the  600  year  cycle  in  the  flood  narrative — that  is, 
while,  upon  some  base  of  calculation,  the  150  days  of  the 
prevalence  of  the  flood  was  the  correction  of  the  600  year 
period,  denoted  by  the  beginning  of  the  rain  of  40  days  + 
no  days  of  the  bearing  up  of  the  ark,  this  very  subdivision 
of  time  was  also  to  denote  a  point  of  the  year  in  which  the 
correction  should  be  marked,  as  thereafter  to  be  the  close 
of  one  and  the  beginning  of  another  year. 

(2.)  The  detailed  relations  of  the  flood  are  interesting. 
As  usual  in  Hebrew,  there  were  diff'erent  words  expressive 
of  the  same  idea  in  the  English  translation.  The  word 
''flood''  is  used  in  various  places,  but  the  special  word  in 
Genesis  is  tnabtil,  or  m'bul.  The  root  word  is  bul,  and  this 
was  the  name  of  the  month,  or  sign,  of  the  occurrence  of 


246  Appendix  V.  ^93- 

rain,  or  of  the  rm'ny  j/wni/i ;  and,  as  one  of  the  moon, 
run  from  the  new  moon  of  November  to  that  of  December 
(Fuerst.)  This  month  is  set  down  as  the  eighth  in  the  Jew- 
ish calendar,  or  it  was  probably  the  third  month  of  the  an- 
cient year,  extending  to  the  winter  solstice,  or  birthplace 
of  the  year;  just  where,  for  correction,  the  stop  should  be 
made — viz.,  at  the  end  of  the  old  year,  by  the  ark  being 
raised  up  from  the  earth  so  that  the  earth  might  pass  on 
under  it,  while  it  remaining  still,  or  slop,  or  JVoah,  would 
at  last,  with  the  sinking  of  the  waters,  drop  at  that  time,  and 
place,  on  the  earth,  where  the  signs  were  thus  made  to  be- 
come correct  with  the  seasons.  This  place  was  similar  with 
our  Easter  period,  which,  regulated  by  lunar  time,  oscillates 
between  certain  fixed  solar  limits.  The  count  for  correc- 
tion of  the  great  calendar  period  of  600  years,  run  from 
the  entering  the  ark,  or  box,  and  continued  150  days ;  but 
this  latter  space  of  time  was  divided  for  some  reason. 
There  is  a  count  from  the  17th  day  of  the  second  month 
(sun  in  Scorpio)  of  40  days,  which  would  carry  to  the  27th 
day  of  the  third  month,  or  Bui,  or  the  solstice  month,  as 
presented  on  the  Egyptian  charts.  It  looks  as  if  the  word 
for  -flood  had  reference  to  this  month  word  ;  and  apparently 
this  view  is  confirmed. 

(3.)  Noah  entered  the  ark,  or  Theba,  or  box,  on  the 
second  (2d)  month,  the  17th  day  of  the  month.  Referring 
to  Seyffarth's  Chronology  (p.  211)  he  says:  "November 
8th,  Julian  style,  i.  e.,  17th  day  of  2d  month,  the  deluge 
commences  in  the  600th  year  of  Noah."  It  seems  that 
Epiphanius  specifies  the  date  on  which  Jesus  received  his 
baptism  at  the  hands  of  John,  on  the  8th  November  like- 
wise, so  that  Jesus  went  down  into  the  water,  or  type  of  the 
pit,  or  womb,  or  of  death  and  birth,  on  the  anniversary  of 
Noah's  going  down  into  the  hollow  of  the  ark.  Seyffarth 
(same,  p.  182)  says  : 

"  The  baptism  of  Christ,  and  the  beginning  of  his  prophetic 
ministry,  are,  first  of  all,  determined  by  the  testimony  of  St. 
Luke.  For,  since  the  fifteenth  year  of  Tiberius,  in  which  the 
Baptist  entered  upon  his  prophetic  ministry,  is,  by  our  present 


§  93-  Appendix  V.  247 

calculation,  brought  down  two  years  later  (than  by  Petavius), 
Christ  must  have  been  baptized  in  the  29th  year  after  the  com- 
mencement of  our  era,  'at  an  age  of  nearly  (wot/)  thirty,'  to  enter, 
forty  days  latcr^  upon  his  prophetic  office.  On  the  same  day, 
the  23d  December,  Christ  was  thirty  years  of  age  ;  and  as  Christ 
was,  as  he  says,  '  born  under  the  law,'  and  consequently  obliged 
to  enter  the  priestly  office  on  the  first  day  of  the  31st  year,  he 
must  have  commenced  his  public  ministry  on  the  22d  of  Decem- 
ber, A.  D.  29,  and  received  his  baptism  on  the  13th  November 
(that  is,  40  days  earlier).  Epiphanius  specijies  the  ?>th  Novem- 
ber^ simply  because^  on  account  of  the  shfting  of  the  epagome- 
nai  {the  intercalary  days)  his  8th  November  corresponds  with 
our  i-^th.'' 

This  quotation  is  made  to  show  how  the  40  days  from  the 
8th  November  terminated  at  the  limit  of  the  22d  day  of 
December,  of  our  day,  the  point  of  the  winter  solstice, 
under  the  explanation  of  Seyffarth,  of  the  correspondence 
of  the  8th  day  of  November  of  Epiphanius,  and  the  13th 
November  of  the  solar  year,  by  use  of  the  five  intercalary 
days ;  which  would  go  to  show  that,  by  Epiphanius,  the 
360  year  period  closed  November  8th  of  the  solar  year,  or 
the  17th  day  of  the  2d  month,  then  by  blotting  out  or  re- 
serving from  count  five  days,  the  17th  day  would  continue 
over  this  period,  so  that  it  (the  17th  day)  would  correspond 
with  the  13th  day  of  November  of  the  solar  year.  Just 
what  has  been  said  above  as  the  count  on  a  circle  of  one 
kind  (360)  stopping,  the  days  thus  blotted  out  would  still 
be  counted  on,  on  the  circle  of  another  kind  (365)  ;  in  this 
case  to  the  commencement  of  the  flood. 

(4.)  Now,  Noah  entering  the  ark  on  this  I7lh  day  of  the 
2d  month,  or  the  13th  of  November,  solar  year  time,  it 
rained  40  days,  the  ark  not  as  yet  being  lifted  up.  At  the 
end  of  40  days  the  ark  is  lifted  up,  and  at  the  end  of  150 
days  from  the  beginning  of  the  flood  (the  full  correction  of 
the  600  year  period),  or  no  days  after  the  end  of  the  40, 
it  descends  on  the  peaks  of  the  mountains,  which  could  not 
have  been  very  high,  as  the  depth  of  the  flood  is  stated  at 
15  cubits,  or  25 -f-  feet.  This  arrangement  is  simply  to  de- 
signate where  in  the  year  the  landing  was  to  take  place, 


248  Appendix  V.  §  93. 

viz.,  December  22d,  the  winter  solstice,  for  it  is  to  be  con- 
sidered that  it  was  at  that  point  when  it  was  lifted  up,  and 
afterward  simply  remaining  stationary,  while  the  earth 
passed  on  under  it,  the  remainder  of  the  time  of  the  150 
days — vizo.  no  days — was  perfected,  or  brought  to  a  close, 
the  waters  abated,  and  the  ark  made  its  landing  on  the 
22d  of  December  of  the  solar  year,  the  winter  solstice. 
This  then  was  the  great  turning  point,  or  arpoipa'to:;,  or 
hinge,  fastened  by  the  flood  calculation,  in  a  calendar  way. 
(It  is  to  be  noted  here,  what  is  constantly  the  case,  that  the 
data  connected  with  the  working  out  of  some  one  particular  phase 
seems  to  be  fitted  for  radiating  off  to  the  accomplishment  of  some 
other  or  others.  The  number  no  is  extraordinary  in  other  rela- 
tions. Joseph  died  in  Egypt,  being  "an  hundred  and  ten  years 
(no)  old ;  and  they  embalmed  him,  and  he  was  put  in  a  box,  or 
ark,  in  Egypt."  (Gen.  50,  26.)  The  narrative  of  his  burial  is 
reserved  to  24th  Joshua,  32,  as  it  were,  to  be  mentioned  in  con- 
nection with  the  death  of  Joshua,  the  son  of  Nun,  of  whom  it 
says,  in  the  29th  verse,  that  he  "  died,  being  an  hundred  and  ten 
(no)  years  old;"  showing  a  bringing  together  of  this  number 
1 10,  thus  twice  used,  and  once  as  connected  with  an  ark  or  Theba. 
So,  as  to  this  number:  365  — 354^  u  ;  and  365  X  n  =4015? 
and  355  X  1 1  =  3905  ;  and  4015  —  3905  =  1 10,  this  very  number. 
This  shows  some  subtle  use,  as  to  which  Joshua,  as  the  son  of 
Nun^  or  565  =  113  X  5?  niay  have  been  connected.  It  has  been 
shown  that  27  -f-  217  ^=  245  days-f-  \\$  (Cain)  =360.  Taking 
the  same  ground  form,  27-1-217  =  245  days -|- no  days  =  355 
days,  or  the  Dove  year,  or  71  X  5  ;  and  this  is  probably  the  use 
of  the  no) 

Other  number  Rests,  or  Stops,  in  the  Flood  Narrative. 

(e.)  It  is  a  curious  matter  to  mark  some  of  the  other 
uses  of  the  number  rests  in  the  description  of  the  flood. 

"The  history  of  the  deluge  is  based  upon  the  solar 
months  of  30  days  each"  (Seyff'arth,  Chronology,  p.  170), 
with  which  statement  the  foregoing  workings  agree.  From 
the  isl  day  of  the  ist  month,  therefore,  to  the  17th  day  of 
the  second  month,  was  47  days.  The  flood  prevailed 
150  days.  Then  the  raven  and  dove  were  sent  forth, 
the  dove  returning.     A  lapse  of  7  days.     The  dove  was 


§  93-  Appendix  V.  249 

sent  forth  again,  and  returned  with  the  olive  branch — i  day. 
Then  a  lapse  of  7  days.  That  is,  in  all,  47  +  150 -[-40 -f- 
7-(-i-|-7  =  252  days.  Then,  to  make  a  full  solar  year  of 
365  days,  would  require  the  additional  number  of  113,  or 
the  famous  diameter  value  of  355,  or  the  Hebrew  word  for 
year.  But  to  make  this  year  of  355  days  would  require 
an  additional  number  of  103,  or  one-half  of  206,  one  of 
the  lengths  of  the  queen's  chamber. 

If,  however,  instead  of  following  the  count  thus,  in  days, 
as  mentioned,  the  months  and  days  be  taken,  then — 
"  On  the  tenth  month,  were  the  mountains  seen  ;" 

10  months,  300  days. 

*'And  it  came  to  pass  at  the  end  of  forty  days,"      40    " 
"And  he  stayed  yet  other  seven  days,"  7     " 

Dove  sent  out  and  returns,  i  day. 

A  lapse  of  seven  other  days  to  the  end,  7  days. 

Or  a  total  of  355     " 

which  is  the  lunar  year  circle  itself;  precisely  a  similar  oc- 
currence with  that  of  the  sums  of  the  ages  of  Abram  and 
Isaac,  being  355,  showing  a  power  of  unification  of  many 
various  matters  with  one  concrete  form. 

The  JVtimber  Values  of  the  Birds. 

(y.)  The  term  Raven  is  used  but  once,  and  taken  as 
cth-h'  orebv,  ^"l^nTl^^  =  678,  or  113  X  6?  while  the  Dove 
is  mentioned  five  times.  Its  value  is  71,  and  7^X5=  355- 
Six  diameters,  or  the  raven,  crossing,  would  divide  the  cir- 
cumference of  a  circle  of  355  into  12  parts  or  compart- 
ments ;  and  355  subdivided  for  each  unit  by  6,  would  equal 
213-0,  or  the  head  in  the  first  verse  of  Genesis.  This  di- 
vided, or  subdivided,  after  the  same  fashion,  by  2,  or  the 
355  by  12,  would  give  213-2,  or  the  word  B'rush,  C'J^TD, 
or  the  first  word  of  Genesis,  with  its  prepositional  prefix, 
signifying  the  same  concreted  general  form,  astronomically, 
with  the  one  here  intended.  Moreover,  213  X  2  =  416,  or, 
as  shown,  the  width  of  the  descending  passage-way  into 
the  pyramid. 


250  Appendix  V.  §  93- 

Mount  Ararat,  or  yared,  or  Yard,  and  its  Signijications. 

is"-)  (^')  T'he  mountain  on  which  the  ark  rested  was 
called  Ararat,  and  this  has  been  shown  to  be  Mount 
Jared,  TH*,  or  the  Mount  of  Descent,  a  figurative  expres- 
sion for  the  basic  source  of  calculation  ;  as  it  is  the  square 
yard,  four  of  which,  or  the  one  solar  day  value,  constitute 
the  Adam  form  of  extension  of  the  Garden  of  Eden,  as 
based  on  the  square  of  3  X  3  =9,  and  6  X  6  =  36 ;  the  key 
enlargement  of  the  Parker  and  Metius  forms,  to  work  a 
change  to  the  factor  6,  to  convert  circular  into  astronomical 
and  earth  measures,  in  the  squared  or  plane  form.  Here 
it  would  seem  to  imply  The  Mount  of  Descent,  having 
reference  to  the  like  uses  of  the  various  kinds  of  measures 
found  in  the  pyramid  mass ;  and  it  is  to  be  likened  to 
the  three  mountains  in  one — viz.,  of  Ibarim,  or  heaven- 
dividers,  or  Hebrews;  oi  JVebo,  or  the  wisdom  behind  the 
arch  of  the  sun,  and  of  Pisgah,  or  the  afex  whence  one 
would  stand  to  review,  or  look  down  on,  a  system  of  di- 
visions made,  which  were  those,  combined  in  one,  on  which 
Moses  went  up  to  review  the  astronomical  and  geographical 
work  which  he  had  done. 

The  Place  of  Ararat,  or  Mount  yared,  in  the  Adamic 

Chronology. 

(2.)     Take  the  place  of  Jared  as  the  mount  of  descent,  in 
its  position,  for  another  phase,  in  the  Adamic  chronology. 
As  to  its  order,  it  will  be  thus  found  : 
I.  Adam;  2.  Seth  ;  3.  Enosh  ;  4.  Cainan  ;  5.  Mahaleel ; 

6.  Jared ; 
7.   Enoch;  8.   Methuselah;    9.   Lamech ;  10.   Noah;    11. 

Shem,  Ham,  and  Japhet ; 
where  Jared  stands  as  the  connecting  link  between  two  sys- 
tems of  5.  Two  5s  =  10,  and  10  is  circumference  to  318-f-, 
and  3i8x6=i90-[-)and  190-l-is  diametertoa  circumference 
of  6,  and  6  is  the  factor  connection  between  circular  and  plane 
shapes.  Here  Jared,  or  yard,  or  6^  X  6^  =  1296,  stands 
as  the  center  or  apex  of  the  system.     Curiously  enough,  as 


§  p3-  Appendix  V.  251 

the  6  days  of  the  week,  and  then  the  7th  day,  stand  as  the 
base  of  various  calculations  as  shown  ;  so  here,  Jared,  the 
yard,  and  Enoch,  the  father  of  the  solar  year  (as  365), 
stand,  respectively,  as  the  6th  and  7th  in  the  order  of  this 
table.  Add  the  ages  to  Jared,  inclusively,  and  the  sum, 
nf  the  mount,  to  give  its  character,  in  one  phase,  is 
130  -}-  105  +  90-1-70  +  65  +  162  =  622  years. 
622  \sthe  sumqftwo  men — viz. ,311 +  311  =622  ;  but  while 
311  is  man,  aish,  it  is  also  the  woman,  as  5  +  300  +1+5 
=  311  ;  and,  as  another  form  of  aish  is  113,  we  have  the 
622,  as  exhibiting — 

311— 113. 
or  the  ivoman-man,  ox  man'ivo^nan,  or  hermaphrodite  form 
of  the  source  of  the  Garden  of  Eden,  reproduced,  which, 
in  its  extension  under  the  Adam  form,  we  have  seen  to  be 
Jared,  or  yard,  squared,  and  multiplied  by  4.  Thus  the 
numerical  enunciations  of  the  types  are  seen  constantly  to 
head  the  various  phases;  from  whence,  in  detail,  the  va- 
rious ramifications  arise  from  the  concrete  form.  Reverse 
the  reading  of  622,  as  226,  and  this  is  diameter  to  the  cir- 
cumference of  712,  the  heel  of  Jacob,  and  found  in  the 
queen's  chamber  measures.  The  use  of  113,  as  a  meas- 
ure, is  reinforced  in  its  use  in  the  post-Adamic  chronolog- 
ical table,  where,  of  Pcleg,  it  is  stated  that  in  his  days  the 
earth  was  divided.  The  value  of  Peleg,  ;|^t),  equals  80  + 
30  +  3  =  113. 

Astronomical  Personijlcation. 

(3.)  Thus,  Ararat  is  shown  to  be  Mount  Jared,  or 
yard,  and  also  to  be  the  monumental  sign  of  the  mark  in 
the  year,  of  its  changes  from  old  to  new,  or  of  the  hinge 
or  cardinal  point  of  the  winter  solstice,  or  the  22d  Decem- 
ber. What  is  the  fcrsonijication  of  this?  Is  it  not  Janus 
Bifrons  of  the  Romans?  Who  stood  with  double  face, 
looking  upon  the  past,  and,  prophetically,  upon  the  coming 
year?  If  there  is  any  one  thing  clearly  shown  in  the 
books,  it  is  that  the  Roman  Catholic  Church  holds  Janus 
Bifrons  as  St.  Peter.     It  was  Peter  that  first  hailed  Jesus 


252  Appendix  V.  §  93- 

as  the  Christ.  Christ  founded  the  Church  on  Peter.  Peter 
was  but  a  form  of  Ararat,  or  Mount  Jared,  marking  the 
winter  solstice  as  December  22d.  While  the  triumph- 
ant Christ,  as  Mcshiac,  sat  in  Leo,  holding  under  his  con- 
trol the  cross  (origin  of  measures),  Peter's  place  was  below 
his,  or  at  his  dental,  holding  also  the  cross.  Reference 
to  this  is  certain  under  the  tradition  of  Peter  beinsr  cruci- 
fied  head  down-ward,  as  the  opposite  of  his  Lord.  Peter 
as  a  stone  was  the  cube  of  that  letter  il,  or  5,  by  which  the 
Hebrews  say  that  God  created  all  things.  "  Thou  art  the 
stone,"  and  "  on  this  stone"  are  the  words.  The  Hebrew 
word  for  stone  is  p}<,  abn,  and  reading  the  letters  as  they 
run,  it  is  125  ;  and  125  is  the  cube  of  ^.  Five  and  five  are 
10,  or  the  space  between  the  cherubims,  or  the  cube  of  10. 
See  !  to  make  this  cube  of  10,  or  the  -perfect  one,  uniting 
within  itself  the  perfect  male  and  perfect  female,  in  their 
conditions  as  separated  from  the  hermaphrodite  form,  as 
shown,  requires  just  8  cubes  of  5  each.  But  the  10,  as  the 
perfect  one  was  Jehovah.  Under  the  Noah  form,  this  is 
represented  by  8  persons,  4  males  and  4  females,  going 
into  the  ark,  and  Noah's  name  as  nil,  or  HJ,  is  the  hiero- 
glyph of  this  use.  Then,  Mt.  Ararat,  or  Mt.  Jared,  or  Mt. 
Janus  Bifrons,  or  Mt.  Peter,  or  Mt.  Cubical  stone  of  $, 
xho.  fotmdation  stone,  and  the  winter  solstice  mark  as  the 
2 2d  December,  were  all  one.  The  whole  was  founded  on 
Peter,  or  125,  and  in  building,  8  of  these  cubes  became  the 
10,  ov  perfect  one,  or  Jehovah  (and  for  this  use,  while  (?(5« 
is  125  as  the  letters  run,  by  adding  them  the  sum  is  8); 
and  10  is  circumference  to  the  diameter  318,  which  was  the 
Gnostic  Christ.  How  strange  it  is  that  it  is  left  to  the 
Epistle  of  Peter — i  Ephes.,chap.  3,  verses  20,21  ;  2Ephes., 
chap.  2,  V.  5  ;  and  chap.  3,  v.  6 — to  make  reference  to 
Noah  and  the  Flood.  But  as  to  Jesus,  in  this  connection, 
his  baptism  by  John,  or  the  dove,  in  the  River-Dan,  or  Fish- 
River,  was  an  answering  to  the  entering  of  Noah,  or  Peter, 
into  the  ark.  The  40  days  elapsing  to  his  entering  upon 
his  ministry,  corresponded  to  the   22d  December  mark  of 


§  93-  Appendix  V.  253 

the  lifting  up  of  the  ark,  and  the  place  of  its  descent  no 
days  thereafter,  whereby  all  things  became  new. 

Other  Types  and  Teachings. 

(h.)  The  figures,  or  displays,  however,  of  one  class  of 
problems  were  co-ordinately  made  to  serve  the  purpose  of 
explanation,  or  the  teaching  in  astronomical  figures  of 
others.  A  most  striking  and  far-reaching  teaching  or 
feature  of  the  astronomical  circle  of  the  signs  was  in  the 
conditions  of  the  sun,  agreeably  to  his  station  in  the  signs 
of  his  acquired  power,  and  of  his  death.  The  balanced 
signs  were  Aries,  the  lamb,  and  the  balances,  =0=,  opposite. 
Out  of  Aries,  the  lamb,  the  sun  now  having  acquired  his 
fructifying  power,  enters  the  sign  of  the  Bull,  presided  over 
by  Venus,  the  type  of  love  and  of  germination.  The  bor- 
der of  the  sign  of  the  Lamb,  then,  was  that  of  Taurus. 
Opposite  to  this,  the  sun,  descending  from  the  lower  edge 
of  Libra,  or  the  balance,  entered  into  Scorpio,  presided 
over  by  Mars,  with  his  hasia  (as  Libra  was  by  Cain,  or 
Pater  Zadic,  the  Just  One,  who,  being,  a  Mars  form,  and 
carrying  the  hasta,  as  the  sun  descends  to  the  lower  edge 
of  the  balaYice,  -pierces  it  with  his  spear,  just  as  it  is  de- 
scribed as  to  Abel ;  for  it  is  not  the  word  to  slay,  or  kill,  but 
to  pierce,  that  is  there  used)  ;  the  mark  of  the  use  being  not 
only  to  pierce,  but  also  as  impregnating  the  place  Scorpio, 
or  the  gate  of  the  woman,  or  Delilah,  with  the  germ  of  a 
new  life.  The  whole  type  was  made  to  answer  to  the  life 
of  man.  The  point  of  greatest  anxiety,  and  of  dread  of 
expectancy,  was  of  course  that  in  Scorpio,  or  of  the  death 
of  the  sun.  Personified,  the  tribe  to  which  this  sign  was 
appropriate  was  Dan;  yet  it  was  in  Dan  that  "we  await 
thy  salvation,  O  Lord."  (The  sign  Scorpio,  being  the  gate 
of  the  woman,  is  opposite  to  the  sign  Taurus,  and  they 
meet  at  a  point  in  the  center  of  the  sphere  just  where  they 
arc  met  by  the  line  ef  the  balance  or  Pater  Zadiei)  The 
place  Scorpio  was  the  pit,  or  the  Hebrew  word  TV^,  shiac, 
the  place  of  death,  the  door  of  Hades,  or  of  Sheol.  But 
true  to  the  type,  as  the  sinking  sun  was  held  to  be  a  dead 


254  Appendix  V.  §  93- 

sun,  on  entering  the  door  of  the  devouring  worm,  the  nighty 
or  Lilah,  or  woman,  prepared  to  give  birth  to  the  new  one. 
So,  by  parallelism,  the  soul  only  passed  the  door  as  a 
preparation  for  resurrection  or  new  birth.  In  the  heathen 
representations  of  this  place  of  condition,  under  the  form 
of  a  woman,  over  the  mouth  of  the  womb,  was  drawn  the 
picture  of  the  scull  -with  crossed  bones.  The  symbol  was 
that  of  the  door  of  life,  as  but  a  note  of  change  from  the 
condition  of  death.  As  death  w^as  to  be  considered  the 
greatest  evil,  the  place  was  hateful,  and  considered  bad, 
and  full  oi sin;  so  that  here  all  that  was  evil,  dreadful,  and 
sinful,  was  the  very  accompaniment  of  all  that  was  to  be 
most  hoped  for,  most  delightful,  and  most  enjoyable.  This 
at  once  makes  plain  the  unaccountably  horrid  qualities  an- 
ciently attributed  to  woman,  down  to  as  late  a  period  as  the 
early  church  fathers. 

The  author  of  "The  Origin  and  Destiny  of  Man,"  page 
145,  has  collected  various  holy  statements  as  to  this: 
"  Corpus  mulieris  ignis  est,"  says  a  holy  person.  O  malum 
et  acutissimum  telum  diaboli,  mulier  1  exclaims  St.  Chry- 
sostom  ;  Per  mulierem  Adam  in  Paradiso  diabolus  pros- 
travit,  et  de  Paradiso  exterminavit.  St.  Augustine  says  : 
Mulier  docere  non  potest,  nee  testis  esse,  neque  fidem 
dicere,  neque  judicare,  quanto  magis  non  potest  imperare? 
St.  John  of  Damascene  says;  Mulier  jumentum  malum, 
vermis  repens,  atque  in  Adamo  domicilium  habens,  men- 
dacii  filia,  Paradisi  custodia,  Adami  expellatrix,  hostis 
pernitiosa,  pacis  inimica.  St.  Peter  Chrysologus,  Bishop 
of  Ravenna,  says  that  she  is  malis  causa,  peccati  auctor, 
sepulchri  titulus,  inferni  janua,  et  lament!  necessitas  tota. 
St.  Anthony  :  Caput  peccati,  arma  diaboli.  Cum  mulierem 
vides,  says  he,  non  hominem,  non  belluam,  sed  diabolum 
esse  credite.  Her  voice  is  serpentis  sibulus.  St.  Cyprian 
would  sooner  hear  basilicum  sibilantem,  than  a  woman 
singing.  St.  Bonaventura  compares  women  to  the  scor- 
pion, which  is  always  ready  to  sting  man.  They  are,  he 
says,  arma  et  balista  diaboli.  Eusebius  of  Cassarea  says 
that  woman  is  saggita  diaboli.     Gregory  the  Great :  Mulier 


§  93-  Appendix  V.  255 

recta  docere  nescit.  St.  Jerome  :  Si  mulicr  suo  arbitrio 
relinquatur,  cito  ad  deteriora  delabitur.  And  again  :  Op- 
tima foemina  rarior  est  phoenice.  And  again :  Janua 
diaboli,  via  iniquitatis,  scorpionis  percussio,  nocivum  genus. 
The  church's  opinion  of  women  would  be  something  fearful 
to  contemplate,  in  connection  with  the  necessity  of  their 
being  the  only  mothers,  sisters,  and  refining  companions 
of  man,  were  it  not  that  this  opinion  was  taken  from  these 
ancient  glyphs  and  unificating  necessities. 

The  word  tl''^^,  s/ii'ac,  is  in  Hebrew  the  same  word  as  a 
verbal,  signifying  lo  go  down  into  the^it.  As  a  noun,  it  also 
means  _^//,  -place  of  thorns ;  also,  the  complaining  word. 
The  hijil  participle  of  this  word  is  PT^JTO,  or  Messiach,  or 
the  Greek  Mcssias,  or  Christ,  and  means  ^'-  he  who  causes  to 
go  down  into  the  ^it^^  a  manifest  attributed  function  of  the 
Savior  as  held  by  Christian  teaching.  A  very  careful 
analysis  and  comparison  of  the  Hebrew  and  Greek  forms 
leads  to  some  almost  astounding  developments,  as  to  the 
twofold  conditions  of  the  Messianic  character.  Nork  says 
most  truly  of  Jesus,  that  he  never  was  anointed  either  as 
high  priest  or  king,  where  he  is  showing  that  the  term 
Christ  is  not  applicable  to  him  as  the  one  anointed,  as 
high  priest  or  king.  A  setting  forth  of  the  Messianic 
meanings  will  throw  a  flood  of  light  on  the  New  Testa- 
ment narratives.  There  are  two  words  in  the  Hebrew  from 
whence  the  Greek  word  Messiah  can  be  derived.  The 
first  is  the  verbal  HC^D,  mashach,  or  participle  passive, 
mt^D,  Mashiiach,  made  to  read  equivalently  H^J^D,  Ma- 
shiach,  or  Meshiac,  the  very  word  used  by  the  Greeks  for 
Messiah.  This  verbal  means  /#  besmear,  to  anoint  as  with 
oil  in  dedicdtion  (Fuerst).  The  second  word  is  n'tT,  shiac, 
same  with  niC^.  As  a  noun  it  has  the  meaning  oi  fit, 
grave;  hence,  to  sink  as  into  a  -pit  or  grave.  It  also  has  the 
meaning  to  speak;  hence,  as  substantive,  word,  or  speech, 
lamentation ,  grief,  humiliation  ;  further,  to  walk  among 
bushes,  thorns.  The  hifl  participle  of  this  word  is  (1*1^0  = 
Meshiac,  or  Messias,  naturally,  and  without  making  any 
equivalent  change  whatever.     Now,  with  what  has  been 


256  Appendix  V.  §  93- 

said  as  to  the  woman  character,  or  quality  of  the  sign 
Scorpio,  which  is  so  often  confounded  by  the  early  church 
fathers  with  the  woman  ;  especially  as  to  its  being  the  pit 
of  the  grave,  while  it  is  the  vagina,  as  indicating  resur- 
rection, and  new  birth:  and,  with  the  remark  of  uVork, 
that  Jesus  never  was  anointed  as  high  priest  or  king,  take 
this  circumstance  of  his  life  into  consideration — viz.,  He, 
as  viortal,  was  never  anointed  but  once;  then  by  a  woman ; 
and  not  as  high  priest,  or  king;  but,  as  He  said,  '•''She  did 
it  for  my  burial,'"' — which  of  the  two  Hebrew  words  giv- 
ing the  term  Mcshiac  is  most  fitting  and  appropriate?  But 
the  fact  is  there  were  two  Messiahs:  One,  as  causing  him- 
self to  go  down  into  the  pit,  for  the  salvation  of  the  world ; 
this  was  the  sun  shorn  of  his  golden  rays,  and  crowned 
■with  blackened  ones  (symbolizing  this  loss),  as  the  thorns  : 
The  other  was  the  triumphant  Messiah,  mounted  up  to  the 
summit  of  the  arch  of  heaven,  personated  as  the  Lion  of 
the  tribe  of  "Judah.  In  both  instances  he  had  the  cross  ; 
once  in  humiliation  (or  the  son  of  copulation),  and  once 
holding  it  in  his  control,  as  the  law  of  creation,  He  being 
Jehovah.  As  strange  as  this  development  is,  its  strange- 
ness is  enhanced,  when  it  is  to  be  shown  that  the  Greeks 
had  also  a  double  form  of  derivation  to  run  parallel  with 
that  of  the  Hebrew  as  given.  Fuerst,  in  noticing  the  pow- 
ers of  the  two  Hebrew  letters  H  and  11,  likens  the  first  to 
the  smooth,  and  the  second  to  the  rough,  aspirate  of  the 
Greeks,  and  sa3's,  moreover,  that  ll  can  be  taken  as  the 
Greek  ;f.  Then  for  the  double  form  :  In  the  Greek  there 
is  the  word  yj>'uo,  whence  yocazo:;,  to  anoint  with  oil;  there- 
fore equivalent  to  the  Hebrew  M^shiac,  having  the  same 
meaning.  Now,  considering  what  Nork  says,  as  to  there 
having  been  no  such  anointing,  and  what  is  said  as  to  the 
real  anointing  for  burial  by  the  woman,  take  the  equiva- 
lent of  y,  in  the  rough  breathing  (in  fact,  Hadley  gives  y 
as  the  rough  aspirate),  and  we  find  the  word  pr^ac^,  or  ypqat::, 
a  word,  speech  (taken  as  from  ptoi,  and  ipco).  Passing  from 
this  to  the  other  form  of  the  rough  aspirate,  or  y,  and  con- 
sidering these  as  equivalent  forms,  we   do  find  ypdto,  "  in 


§  93-  Appendix  V.  257 

the  earliest  examples  of  the  active,  of  the  gods   and  their 
oracles,   to  give  the  7iccdfiil  answer^  give  a  response ;" 
then  Y.nazijpcoz  (from  xpdio)  of''  or  belonging   to  an  oracle; 
then  '^()-qaz-qi)tov,  the  seat  of  the  oracle^  an  offering  for  the 
oraele,  generally  a   sacr-ficial  victim,  a  sacrifice^  victim. 
Thus  iho.  fated  sacrifice  of  the  word.    Then  came  the  short- 
ened use  of  this  form  in  y^prj<TTO(;  (from  yjiaco),  to  run  -par- 
allel to  y()cazoz.     Thus  the  paralleled  double  form  is  com- 
mon to  both  languages.     While,  also,  this  is   appropriate 
to  the  structure  of  the  Greek  language,  Godfrey  Higgins, 
in  Anacalypsis,  Vol.  i,  p,  569,  gives  authorities  confirming 
the  fact  of  the  double  use  of  the  two  terms  Christos  and 
Chr'estos.     The  learning  is  very  singular,  as  showing  the 
gradual  suppression  and  elimination  of  the  esoterism,  by 
which  Scripture  teaching  has  been  thrown  into  confusion, 
and  its  real  system  has  been  subverted.     The  Greek  of 
I  Pet.  II,  2,  is:  "  If  so  ye  have  proved  that  (xprjazb::  6 
xufJioi;)    Chr'estos  is  the  Lord."     To  prove  that  the  reading 
has    been    that  of  a:  proper  name,    Bishop   Marsh  says : 
"  I    Pet.   II,  3  :    ypr^azo^^  others    ypcaro::."      St.    Paul,   in 
Philipp.  I,  21,  is  made  to  say  :  "  For  me  to  live  is  Christ, 
to  die  is  gain."     Dr.  Jones  says  of  this,  that  the  sense  "  re- 
quires   yjnazoq,  in  the  sense  of  yp-qazo^^  to  correspond  with 
y.zpooci  {gain)."     St.  Paul  seems  to  mean  here,  "  For  me  to 
live  is  death  {yprjozo<:),  to  die  is  to  live  (gain)  ;"  having  ref- 
erence to  the  resurrection  in  Christ,  or  yptazoz-    It  involves 
the  idea  of  5«<;r-ifice,  or  new-birth,  by  death  unto  righteous- 
ness, or  this  very   yprjaro::,  or  M'eshiac,  condition.     Justin 
Martyr  calls  the  Christians  by  name  of  ypr^aztavot.     And 
so  on.     To  a  late  day,  the  terms   Chr'estos  and   Christos 
for  Christ,  were  used  interchangeably.     The  two   condi- 
tions were  necessary  to  the  full  proportions  of  the  whole 
Christian  system.     Jesus,  as  the  siffering  sacrifice,  could 
not  be  the  trium-phant  Christ  until  he  had  passed  through 
the  sacrificial  Chrest  condition.     At  Scorpio,  he  was  Chres- 
tos,  in  the  pit,  among  the  thorns,  or  blackened  rays;  but 
thence,  passing  around  the  circle,  until  the  summit  was  at- 
tained, at  Leo  He  became  the  triumphant  Christos,  as  the 


258  Appendix  V.  §  93' 

Lion  of  the  tribe  of  fudah,  who  had  subdued  all  things 
under  himself.  The  cross  was  common  to  both  conditions — 
once  to  denote  suffering,  and  the  phallus,  and  then  to  de- 
note the  origin  of  measures,  or  Creative  Law,  or  Jehovah, 

The  Meshiac  Condition  connected  with  the  Geographical 
Location  of  the  Head-  Waters  of  the  Jordan  River. 
(/.)  To  the  tribe  of  Dan,  geographically,  was  assigned 
the  place  in  which  were  the  head-waters  of  the  Jordan,  or 
the  River-Dan  The  word,  in  Hebrew,  bears  this  mean- 
ing, and  thus  it  becomes  the  River  of  Judgment  (for  Dafi 
\s  Judge,  or  judgment),  or  Dan,  or  of  Sheol,  or  of  Hades, 
or  of  Styx,  where  was  located  the  place  of  judgment  of  the 
departed  spirits.  Therefore  the  river  Jordan  had  its  head- 
waters in  the  springs  of  Scorpio,  or  the  gates  of  death,  or 
the  vagina  of  the  woman.  Baptisms  in  this  river,  as  can 
he  seen,  were  therefore  bu*^  types  of  the  going  down  into 
the  pit,  and  of  the  resurrection  therefrom.  The  word  Jor- 
dan also  may  bear  the  analysis  of  the  word,  as  11%  tofow 
down,  with  an  appended  |  final,  which  may  be  taken  as 
a  determinative,  in  the  hieroglyph,  of  the  fish;  for  this  let- 
ter is  Nun,  or  fish,  and  thus  determines  the  river  as  the 
Rish  River. 

Now,  it  can  be  seen  how  perfectly  the  Christian  scheme 
was  made  to  answer  to  its  ancient  prototype.  When,  for 
the  first  time,  Jesus  asks  his  disciples,  "Whom  do  men  say 
that  I  the  Son  of  Man  am  ?"  (Son  of  Man  is  the  Ben  Enosh 
of  Daniel,  and  the  Son  of  Seth  (the  year)  in  Genesis,) 
Simon  Peter  (Simon  Bar  Jonah,  or  the  son  of  the  Dove,  and 
also  as  Peter  the  stone,  Abn,  pN,  125,  or  the  cube  of  5, 
or  letter  H,  or  womb)  answered,  and  said  :  "  Thou  art  the 
Meshiac,  the  son  of  the  living  God."  (Matthew  16.)  Now, 
all  this  depends  for  its  real  significance  on  just  that  on 
which  no  stress  would  ever  be  laid  without  instruction. 
Tlie  verse  (13)  is  :  "  When  Jesus  came  into  the  coasts  of 
CcBsarea  Philipfi,  he  asked  his  disciples,  saying,  Whom 
do  men  say  that  I  the  Son  of  Man  am?"  The  location 
gave  rise  to  all  the  rest.     Caesarea  Philippi  was  the  site 


§  93- 


Appendix  V. 


259 


of  ancient  Dan,  out  of  which  very  spot  welled  forth  the 
^reat  spring  of  the  Jordan  river.  He  had  gone  to  the 
localized  type  of  the  pit,  the  gate  of  death,  or  of  Sheol. 
Jesus  in  Dan  was  in  the  shiac,  or  pit.  He  had  caused  to 
go  there,  therefore  He  was  the  H^J^O,  the  Meshiac.  He 
was  enacting  His  going  down  into  the  pit  agreeably  to  the 
ancient  types  and  symbols.  Astronomically,  it  was  the 
death  of  the  sun,  but  a  death  which  was  the  precursor  of 
the  JVczu  Sun.  The  death  planted  life  in  the  womb  of 
darkness,  of  Lilah,  or  of  Egypt,  and  "  Out  of  Egypt  have 
I  called  my  son." 

A  consideration  of  the  salient  dates  in  the  life  of  Jesus 
seems  to  strengthen  the  astronomical  exposition  made. 
From  Seyffarth  is  to  be  gathered  : 

"According  to  solar  months  (of  30  days,  one  of  the  calen- 
dars in  use  among  the  Hebrews)  all  remarkable  events  of  the  Old 

Testament  happened  on  the  days  of  the  equinoxes  and  the  sol. 


stice&4.  for_^nstancej_the  foundations  and  the  dedications  of  the 
temples  atjiLaltars^and  consecration  of  the  taFernacle).    ^n~ 
tHe^mecardinardays,  the  most  remarkable  events  oFthe  New 
Testament  happened  ;  for  instance,  the  ^""t^5^£i£tion^_Uie_birtfi7' 
the"  resurrection  oTXrhnst^  andlhe"  birth  ofTohn  the  Baptist." 
^'"Anmhus  we  learn  that  all  remarkable  epochs  of  the  New  Tes- 
tainent  were  i^pically  sanctified  a  long  time  before  by  the  Old 
Testament,  beginning  at  the  day  succeeding  the  end  of  the  Crea- 
tion, which  was  the"  a^ayof  the  vernal  equinox."     "During  tliF 
crucifixTonTon  the  I4ttrday  orT^Hsan,  Dionysius  Areopigita  saw, 
in  Ethiopia,  an  eclipse  of  the  sun,  and  he  said,  Now,  the  Lord 
(Jehovah)  is  suffering  something."     "Then  Christ  arose  from 


the  dead  on  the  22d  March,  17  Nisatz,  Sunday^jhejiay  of  the 
vernal  equinox  (Seyf.,  quoting  Philo  de  Septen.) — that  is.  on 
Easter,  or  on  the  da^^when  the  sun  gives  new  life  to  the  earth.^ 
cr^g~:;^^;^7-^f^l^nThrBaptist, '  lie  must  increase,  but  I  nvust 
decrease,'  serve  to  prove,  as  is  affirmed  by  the  fathers  of  the 
church,  that  John  was  born  on  the  longest  day  of  the  year,  and 
Christ,  who  was  6  months  younger,  on  the  shortest,"— 22d  June 
and  22d  December,  the  solstices." 

This  only  goes  to  show  that,  as  to  another  phase,  John 
and  Jesus  were  but  epitomizers  of  the  history  of  the  same 
sun,  under  differences  of  aspect  or  condition  ;  and  one  con- 


26o  Appendix  V.  §  93. 

dition  following  another,  of  necessity,  the  statement,  Luke 
ix.,  V.  7,  was  not  only  not  an  empty  one,  but  it  was  true, 
that  which  "was  said  of  some,  that  (in  Jesus)  John  was 
risen  from  the  dead."  (And  this  consideration  serves  to 
explain  why  it  has  been  that  the  Life  of  A^ollomus  of 
Tyana,  by  Philostratics,  has  been  so  persistently  kept  back 
from  translation  and  from  popular  reading.  Those  who 
have  studied  it  in  the  original  have  been  forced  to  the  com- 
ment that  either  the  "  Life  of  Apollonius"  has  been  taken 
from  the  New  Testament,  or  that  the  New  Testament  nar- 
ratives have  been  taken  from  the  "Life  of  Apollonius," 
because  of  the  manifest  sameness  of  the  means  of  con- 
struction of  the  narratives.  The  explanation  is  simple 
enough,  when  it  is  considered  that  the  names  fesus,  He- 
brew J^^  and  Apollonius,  or  Apollo,  are  alike  names  of 
the  sun  in  the  heavens ;  and  necessarily  the  history  of  the 
one,  as  to  his  travels  through  the  signs,  with  the  personifi- 
cations of  his  sufferings,  triumphs,  and  miracles,  could  be 
but  the  history  of  the  other,  where  there  was  a  wide-spread, 
common  method  of  describing  those  travels  by  personifica- 
tion.) It  seems  also  that,  for  long  afterward,  all  this  was 
known  to  rest  upon  an  astronomical  basis ;  for  the  secular 
church,  so  to  speak,  was  founded  by  Constantine,  and  the 
objective  condition  of  the  worship  established  was  that  part 
of  his  decree,  in  which  it  was  affirmed  that  the  venerable 
day  of  the  sun  should  be  the  day  set  apart  for  the  worship 
of  Jesus  Christ,  as  Sun-dixy,  There  is  something  weird 
and  startling  in  some  other  facts  about  this  matter.  The 
prophet  Daniel  {true  prophet,  as  says  Graetz),  by  use  of 
the  pyramid  numbers,  or  astrological  numbers,  foretold  the 
cutting  off  of  the  M'eshiac,  as  it  happened  (which  would 
go  to  show  the  accuracy  of  his  astronomical  knowledge,  if 
there  was  an  eclipse  of  the  sun  at  that  time) ;  which  fastens 
the  event,  say,  of  the  eclipse  of  the  sun  at  that  time.  Now, 
however,  the  temple  was  destroyed  in  the  year  71,  in  the 
month  Virgo,  and  71  is  the  Dove  number,  as  shown,  or 
71  X  5  ^355»  and  with  thefsh,  a  Jehovah  number.  Is  it 
possible  that  the  events  of  humanity  do  run  co-ordinately 


§  93-  Appendix  V.  261 

with  these  number  forms?  If  so,  while  Jesus  Christ,  as  an 
astronomical  figure,  was  true  to  all  that  has  been  advanced, 
and  more,  possibly,  He  may,  as  a  man,  have  filled  up,  under 
the  numbers,  answers  in  the  sea  of  life  to  predestined 
types.  The  personality  of  Jesus  does  not  appear  to  have 
been  destroyed,  because,  as  a  condition.  He  was  answering 
to  astronomical  forms  and  relations.  The  Arabian  says  : 
"Your  destiny  is  written  in  the  stars."  So  also,  in  this 
connection,  while  from  Adam  to  the  flood  was  1656  years — 
a  mark  in  the  reverse  reading  of  the  Parker  astronomical 
square,  or  6561 — the  late  Dr.  Mahan,  in  "Scripture  Nu- 
merals," shows  that,  from  the  establishing  of  the  Levitical 
Dispensation  to  the  destruction  of  the  Temple,  was  also 
1656  years,  or,  reversing  again,  a  terminal  square  of  6561  ; 
thus  showing  the  squaring  out,  or  cornering  out,  of  the 
entire  Dispensation  from  Adam  to  the  destruction  of  the 
temple,  in  the  mystical  values  of  the  measuring  square. 

Other  M'eshiac  Types  and  Shadows. 
(/.)  (i.)  The  application  of  the  same  type  accounts  for 
the  means  of  conversion  of  St.  Paul.  He  was  Saul  of 
Tarsus  before  that  event ;  that  is,  he  was  Shcol,  Hebrew 
for  Saul,  and  Tarsus  was  a  city  founded  by  the  lonims,  or 
the  people  of  the  Dove.  He  was  on  his  way  to  Damas- 
cus, the  pot  of  blood;  and  when  struck  with  blindness,  or 
darkness,  a  type  of  being  in  the  pit,  he  was  in  Dan,  through 
the  territory  of  which  he  had  to  pass  on  his  way.  In  the 
old  pictures  of  the  scene,  he  is  represented  as  being  thrown 
from  a  horse,  falling  backward,  because  of  the  vexing  by 
a  serpent  of  the  horse's  heels  ;  and  the  Bible  says  of  Dan, 
"  an  adder  in  the  path,  that  biteth  the  horse  heels,  so  that 
his  rider  shall  fall  backward."  The  horse  was,  by  reason 
of  his  four  legs,  symbol  of  a  square,  or  of  the  four  cardi- 
nal points,  the  one  bitten  being  of  Scorpio,  or  Dan,  so  the 
serpent  biting  the  heel  carries  back  to  the  Garden  glyph. 
Saul  was  undergoing  the  Meshiac,  or  Chrcst,  condition  ; 
having  passed  out  of  which,  straightway  he  preached  Me- 
shiac, or  Christ,  to  which  he  had  arrived  by  his  initiation  ; 


262  Appendix  V.  §  93. 

and  afterward  his  name  is  changed  to  Paul,  the  Little  (so 
said),  or  smaller  type  of  Christy  having  dropped  the  Sheol 
characteristic. 

It  must  be  borne  in  mind  that  our  present  Christianity  is 
Pauline,  not  Jesus.  Jesus,  in  his  life,  was  a  Jew,  con- 
forming to  the  law;  even  more,  He  says:  "The  scribes 
•and  Pharisees  sit  in  Moses'  seat ;  whatsoever  -therefore  they 
command  you  to  do,  that  observe  and  do."  And  again  : 
"  I  did  not  come  to  destroy,  but  to  fulfil  the  law."  There- 
fore, He  was  under  the  law  to  the  day  of  his  death,  and 
could  not,  while  in  life,  abrogate  one  jot  or  tittle  of  it. 
He  was  circumcised  and  commanded  circumcision.  But 
Paul  said  of  circumcision  that  it  availed  nothing,  and  he 
(Paul)  abrogated  the  law.  Saul  and  Pc?z^/— that  is,  Saul, 
under  the  law,  and  Paul,  freed  from  the  oblifrations  of  the 
law — were  in  one  man,  but  parallelisms  in  the  Jlcsh,  of 
Jesus  the  man  under  the  law  as  observing  it,  who  thus  died 
in  Chr'estos  and  arose,  freed  from  its  obligations,  in  the 
spirit  world  as  Christos^  or  the  triumphant  Christ.  It  was 
the  Christ  who  was  freed,  but  Christ  was  in  the  spirit.  Saul 
in  the  flesh  was  the  function  of,  and  parallel  of,  Chrestos. 
Paul  in  the  flesh  was  the  function  of,  and  parallel  of  Jesus 
become  Christ  in  the  spirit,  as  an  earthly  reality  to  answer 
to  and  act  for  the  afothcosis ;  and  so,  armed  with  all  au- 
thority in  the  flesh  to  abrogate  the  human  law. 

(2.)  The  same  types  are  to  be  seen  in  the  histories  of 
Saul  and  David.  Saul  was  Sheol,  the  son  of  Kish  (or  of 
113).  By  name  he  was  Hades,  or  the  pit,  as  Paul  was 
under  his  Saul  name.  He  was  the  type  of  the  going  down, 
and  down  he  went.  David,  on  the  other  hand,  was  the 
ruddy  blooming  youth,  growing  in  his  strength  to  the  be- 
coming the  Lion.  The  types  are  Aries,  Leo,  and  Dan. 
The  determinatives  of  the  types  are,  in  part,  as  follows : 
Saul  was  taken  to  be  king  while  hunting  for  his  father's 
asses,  while  David  was  taken  to  be  king  from  following  his 
father's  flocks  of  sheep.  The  sheep  mark  was  the  sym- 
bol of  the  sun  in  Aries ;  while  the  ass  was  the  symbol  of 
Typhon,  or  the  devil,  lord  of  the  descendant. 


§  93-  Appendix  V.  263 

(3.)  The  acrostic  use  is  to  be  found  in  the  mysteries  of 
the  Bible.  The  nth  verse  of  the  96th  psalm  is  an  in- 
stance of  this  kind  : 

"  Let  the  heavens  rejoice  and  the  earth  be  glad."  The 
first  letters  of  the  words,  put  together,  form  the  great  word 
mn%  or  Jehovah.  This  play  upon  words  is  confirmed  as 
proper  by  Christian  usage,  in  the  acrostic  forming  the  z'c/i- 
thiis,  ox  fish  ^  as  Christ. 

As  the  words  *'  Shem,  Ham,  and  Japhet,"  have  been 
shown  to  be  determinatives  of  the  pyramid  structure,  so 
they  are  t3^pes,  setting  forth,  by  way  of  acrostic,  the  Jesus 
and  the  Christ  meanings.  Tiie  first  letters  of  the  names 
are  S,  H,  and  I. 

(i.)  These,  read  in  the  reverse,  are  IHS,  the  mono- 
gram of  Christ,  as  given  by  St.  Barnabas.  The  values 
are,  by  adding,  equal  to  318,  and  this  is  the  numerical 
value  attributed  to  Christ  by  St.  Barnabas,  meaning  a  di- 
ameter to  a  circumference  oi  one. 

(2.)  Placed  agreeably  to  the  reading  of  318,  and  the 
arrangement  of  the  letters  becomes  changed  to  SIH,  or 
n^t^,  Hebrew  shiac,  the  pit,  or  source  of  the  Meshiac. 

(3.)  Changing  the  breathing,  and  the  11  becomes  H,  or 
changed  into  the  Latin  or  Greek  e,  and  there  results  lES, 
or  Jes-Ms,. 

(4.)  If  the  character  values  of  IHS  are  taken  in  the  re- 
verse, they  are  381,  the  half  base  side  of  the  pyramid. 

Jesus  was  I-am  before  Abraham  was  born.  But,  further, 
since  the  shiac  was  the  fit,  and  the  pit  was  in  the  sign 
Scorpio,  and  the  shiac  is  convertible  into  IHS,  one  great 
monogram  of  Christ,  the  whole  becomes  explanatory  of  the 
great  badge  of  the  Roman  Catholic  Church  ;  and  which, 
according  to  Godfrey  Higgins  (Anacalypsis,  Vol.  II., 
p.  202),  is  placed  on  the  breast  of  the  Pope.    The  badge  is — 


or  it  is  the  monogram  of  the  earthly  condition  of  the  repre- 


264  Appendix  V.  §93- 

sentative  of  the  spiritual  Christ.  It  is  the  Jesus  condition 
of  Chr'estos,  or  y^cir^aroc,-,  or  descender  into  the  pit,  under  the 
astronomical  sign  Libra.  The  sign  Scorpio,  which  is  that 
of  the  Shiac,  this  birthplace,  or  causer  of  the  Christ  con- 
dition, is  directly  under  and  bordering  on  Libra.  Hence 
the  glyph.  The  Church  temporal — i.  e.,  every  member 
thereof — headed  by  the  Pope,  must  obey  this  sign  before 
assumption  can  be  made  of  the  blessed  Christ  condition. 


§  94-  Appendix  VI.  265 


APPENDIX  VI. 

Grand  Determinative  at  the  Close  of  the  Flood. 

§  94.  (a.)  The  grand  work  of  construction  of  the 
means  of  setting  forth  the  creative  law  of  God,  both  as  to 
the  measures  of  the  heavens  and  the  earth ;  of  the  ways 
of  sh.owing  man's  spiritual  obedience  to  this  miinhcr  law 
of  creation  ;  and  of  laying,  through  this  law,  the  founda- 
tion for  the  power  of  prophetic  utterance,  was  finished. 
Then  came  a  grand  explanatory  determinative,  showing 
that  the  scope  of  the  knowledge  of  this  creative  law  was 
tmivcrsal.  It  was  not  confined  to  any  one  part  of  the  earth 
exclusively.,  but  belonged  to  all  peoples  and  to  all  races. 
This  knowledge  was  a  commonality  for  the  guidance  of  the 
world.  Briefly,  the  Great  Book  discloses  a  secret  in  the 
eleventh  chapter  of  Genesis.     The  first  words  are  : 

"And  all  the  earth  was  of  one  lip,  and  of  one  form  of 
making  an  orderly  use  of  the  -power  letters  or  numbers  of 
the  alphabet ;"  where  the  basic  word  for  an  orderly  string- 
ing together  of  words  or  syllables  into  one  whole  (see 
Fuerst,  under  ")D"T),  as  might  be  expected,  is  the  Logos 
word  "HDI,  or  ddbvar,  or  206;  and  where  the  power  of 
enunciation  is  termed  lip,  to  denote  merely  the  instru- 
mentality of  the  voice,  as  one  mode  of  expression  of  the 
uses  of  206,  or  of  the  1D1. 

The  inhabiters  said,  one  to  another,  Let  us  build  us  a  ^ 

tower.  What  for?  Architecturally  to  set  forth  the  same 
problem,  just  finished.  From  the  narrative  one  would  sup- 
pose that  they  did  build  the  tower,  but  not  completel}'-  the 
city.  Then  it  is  said  :  "And  the  Lord  said,  The  people  is 
one,  and  they  all  have  one  lip.  ...  Go  to,  let  us  go 
down,  and  there  confound  their  lip,  that  they  may  not  un- 
derstand one  another's  lip."     What  is  determined?     Not 


266  Appendix  VI.  §  94- 

that  their  knowledge  of  the  dabvar,  or  206,  or  of  the 
creative  law^  was  to  be  confounded,  but  simply  that  their 
means  of  expression  by  lip,  or  voice,  of  this  knowledge 
should  be  diversified  into  different  forms  of  oral  communi- 
cation. All  had  the  like  knowledge,  but  by  confusion  of 
lip,  one  part  became  Phenician,  or  Chaldee,  or  Egyptian, 
or  Etruscan,  or  Pelasgic,  and  so  on.  It  is  most  likely  that 
some  one  portion  held  to  the  original  form,  and  the  Phe- 
nician seems  to  have  been  that  form.  But,  notwithstand- 
ing this  confusion  of  oral  expression,  the  lesson  is  taught 
that  the  esoterisms  displayed  in  the  Hebrew  Bible,  were 
likewise  the  property  of  other  races  ;  and  this  abundantly 
displayed  even  in  our  day.  Of  course,  it  is  not  a  matter 
for  discussion  here,  as  to  how  greatly  this  esoteric  knowl- 
edge might,  or  did  become  confused,  or  even  perhaps, 
among  some  peoples,  lost. 

An  Evidence  of  Common  Possession. 

(b.)  An  evidence  can  be  furnished  of  the  commonality 
of  this  knowledge,  in  such  form,  also,  as  to  guide  toward 
unravelingthe  Bible  glyphs.  The  thought  of  the  ancient  Jew 
may,  perhaps,  have  been  to  spurn  the  devotee  of  Bacchus 
as  an  idolator ;  and  perhaps,  at  that  time,  he  was.  But 
see  :  Bacchus  was  saved  out  of  the  waters  of  the  Nile,  in 
an  ark,  by  lo,  or  Ino,  the  daughter  of  Luna.  Such  was 
the  tradition.  Moses  was  saved  out  of  the  same  waters  by 
the  daughter  of  Pharaoh.  The  mystery  begms  to  clear 
away,  as  also  the  distinction,  when  the  numerical  meaning 
of  the  name  Pharaoh,  H^Dfi,  is  known  to  be  355,  or  the 
value  of  that  circular  term  of  the  Hebrews,  s/iana/i,  njlT 
(equals  355),  f^e  name  of  the  lunar  year  period.  The 
serpent,  symbol  of  ever  revolving  time,  swallowing  one 
unit  of  its  length  of  355,  becomes  354,  the  ancient,  or  He- 
brew, or  Egyptian,  or  Pharaoh  lunar  year.  The  daughter 
of  Pharaoh,  then,  was  the  daughter  of  the  lunar  year,  or 
of  Luna,  equally  with  the  savior  of  Bacchus.  The  power 
of  explanation  is  in  that  the  pagan  glyph  is  less  obscured 


§  94-  Appendix  VI.  267 

than  the  Hebrew  one,  inasmuch  as  a  lunar  quality  is  plainly 
given  ;  but  once  taken,  the  Hebrew  is  by  far  the  most  valu- 
able, inasmuch  as  it  gives  the  very  value  of  the  quality — 
viz.,  355  — 1:=354.  Faintly,  the  mission  of  Moses  before 
Pharaoh  can  now  be  disclosed.  Moses  stands  before  the 
pyramidal  flame.  His  name,  TM^D,  equals  345.  To  what 
the  value  refers  is  a  mystery.  It  may  be  taken. as  the 
radius  of  the  elements  of  circle  three,  §  82  (3.),  as  connected 
with  the  pyramid  interior  works  ;  or  as  the  numbers  3 — 4 — 5 , 
for  the  sides  of  a  right-angled  triangle ;  or  as  435,  for  217 
X  2  ;  or  it  may  be  taken  in  connection  with  the  problem  of 
Mr.  Myers,  given  in  his  Quadrature,  connected  with  7^  = 
49  -f  I  =:  50  (and  as  to  which  there  is  curious  rabbinical 
learning  in  Land  Marks  of  Free  Masonry,  Vol.  2,  p.  432, 
note,  London  ed.)  The  pyramidal  flame  may  involve  the 
word  s/iadd/,  HC^,  the  god-name,  as  318  (T  doubled  by 
dagcsh),  or  314,  diameter  to  a  circumference  of  one.,  and 
circumference  to  a  diameter  oi  one;  the  mean  being  316,  a 
great  value  connected  with  the  foot  of  the  descending 
passage-way  in  the  pyramid,  or  381.  The  Lord,  or  Jeho- 
vah (a  diameter  value  growing  out  of  113,  and  the  perfect 
one  of  a  denomination  of  20612),  appears  to  him.  He  says 
he  has  selected  him  to  go  before  Pharaoh,  or  355,  the  cir- 
cumference of  113.  As  a  proof,  he  tells  him  to  throw  the 
rod  (a  diameter)  he  has  in  his  hand  (value  5)  down  upon 
the  ground  (113  X  5  =  565  =  TV\T\,  or  Eve,  or  woman  half 
of  Jehovah).  It  becomes  a  serpent.  He  tells  him  to  take 
it  by  the  tail  (the  value  5  for  hand  is  also  the  letter  H,  or  the 
womb,  and  taking  the  tail  of  the  serpent  in  the  hand  is 
equivalent  to  the  process  of  making  the  year  scale,  as 
365 — 5  ='360  —  5  =  355),  and  it  is  now  the  year  value. 
But  having  done  so,  it  becomes  again  a  rod,  or  diameter 
value,  or  the  lesson  is  taught.  Here  are  numbers,  values, 
and  symbols  of  the  calculations,  in  terms  of  the  lunar  year 
values,  for  the  serpent  is  one  symbol  for  the  calculation  of 
the  lunar  year  in  the  terms  of  the  values  113  :  355.  With 
these,  Moses  is  to  go  before  Pharaoh,  who  is  the  lunar  year, 
as  355- 


268  Appendix  VI.  §  95- 

Egypt  was  darkness,  or  the  womb,  or  mother,  in  oppo- 
sition to  Mount  Zion,  which  was  male.  It  was  out  of 
Egypt  that  God  deigned  to  "  call  his  son."  (Seyf.  Chro., 
p.  191.)  She  was  the  woman  of  the  garden,  or  rather  the 
garden  itself,  whose  number  was  that  of  the  7th  day,  or  7, 
and  which  was  based  on  113  :  355.  The  river  Nile  was 
one  of  the  passage-ways  from  the  center  of  the  garden,  or 
the  place  of  the  birth  of  time.  Pharaoh,  or  355,  was 
Egypt,  because  he  was  lord  of  Egypt ;  and  Moses  was  the 
calculator,  or  Hermes.  Again,  from  these  connections,  it 
now  becomes  plain  why  Solomon  (the  son  of  Shcbu,  or  7, 
and  who  afterward  entertained  the  queen  of  darkness,  or 
S/icdd),  together  with  his  other  buildings,  erected  a  porch 
(type  of  revolving  time  or  aeon)  for  Pharaoh's  daughter, 
adjoining  his  judgment  (Dan)  hall.  It  is  but  a  figure  for 
calculations  of  time,  the  hall  of  judgment  being  the  place 
of  Hermes,  or  the  Egyptian  Thot,  the  god  of  knowledge, 
and  the  calculator.  It  is  possible  that  light  is  thrown  by 
the  Moses  glyph  upon  the  shipwreck  of  St.  Paul.  Paul 
shipwrecked,  while  kindling  a  fire,  the  rods  or  sticks  being 
in  his  hand,  a  serpent  escaping  from  the  flame  (mystic), 
or  pyramidal  sun  measure,  wraps  itself  around  his  fore- 
arin.  Here  seems  to  be  the  recurrence  of  the  type  under 
a  change  of  form,  after  a  fashion  approximating  the 
fpkillin  use,  a  note  as  to  which  is  to  be  found  in  the  con- 
clusion to  these  appendices. 

The  Construction  of  the  Tahcrnaclc. 
§  95.  The  greatest  expansion  from  the  Garden  of  Eden 
(on  and  in  which  it  is  rabbinically  said  that  the  whole  law 
rests,  but  that  its  containments  are  too  subtle  to  be  found), 
architecturally,  was  the  tabernacle,  which  Moses  built  just 
after  his  serpent  exhibitions  before  Pharaoh.  In  various 
places,  especially  see  Smith's  Dictionary  of  the  Bible, 
where  a  most  beautiful  eye-pleasing  structure  is  framed, 
and  the  Bible  correctcdhy  an  F.R.S.,  descriptions  of  the 
tabernacle  are  to  be  found,  as  an  apparently  pleasing  tent 
structure  to  the  eye ;  but  a  careful  reading  of  its  descrip- 


§  95-  App5;ndix  VI.  269 

lion  in  Exodus,  with  an  attempt  to  put  it  together,  will  cor- 
rect the  ardent  desire  of  most  to  have  of  it  a  stylish  oriental 
structure.  They  will  soon  see,  who  try  this,  that  the  setting 
forth  and  combining  of  measures  was  the  object  of  the 
mention  and  detail  of  its  various  parts.  The  grand  object 
of  this  tabernacle  wms  that  it  should  be  a  residence  of  Je- 
hovah. Now,  the  work  was  made  up  by  the  offerings  of 
the  people.  There  were  just  603550  people  enumerated  as 
offering  a  helcah  apiece.  There  were  two  bekahs  to  the 
shekel;  therefore,  there  were  offered — 

603550  -^  2  =  301775  shekels. 
But  there  were  3000  shekels  to  the  talent.     So  there  were 
just- 
In  talents,  100.00 
With  remainder  over,  of,  in  shekels,           1775.00 

It  may  be  stated  in  another  way.  There  being  603550 
bekahs,  there  being  6000  bekahs  to  the  talent,  then  there 
are  100  talents,  with  a  remainder  over  of  3550  bekahs 
(where  the  use  of  113  :  355  crops  out  as  1130  :  3550, 
where  11 30  is  circumference  to  a  diameter  of  360).  3550 
shekels  -^  2  =  1775  shekels,  as  above. 

This  was  the  actual  division  made ;  for,  of  the  100  tal- 
ents were  made  the  sockets  of  the  pillars,  and  of  the  re- 
maining 1775  shekels  were  made  the  hooks  of  the  pillars. 
These  last  words,  the  hooks  of  the  fillars, 

are  said  to  be  of  very  great  kabbalistic  value  ;  so  much  so  (it  is 
said)  that,  in  the  scrolls  of  the  law,  the  commencement  of  a 
section  is,  where  possible,  made  by  the  letter  r-a?/,  the  f  age 
itself  being  considered  as  the  omudim;  because,  it  is  said  of 
them,  that  they  carry  the  key  power  of  the  tabernacle  con- 
struction. By  the  same  authority,  it  is  said  that  the  word 
DmiDI^,  omudim,  can  be  taken  as  meaning  cubits;  hence  a 
meaning  oi  mother  diwd  fore- arm.  In  one  way,  apart  from 
this  departure,  the  difficulty  is  not  very  great,  with  the  helps 
we  have  of  construction.  The  house  was  to  be  the  place 
of  residence  of  Jehovah,  and  Jehovah  is  but  a  play  on  the 
value  113,  or  diameter  to  a  circumference  of  355,  or  Pha- 


270  Appendix  VI.  §  95. 

raoh ;  while  it  is  also  the  value  of  the  straight  line  one,  of 
a  denomination  of  20612.     We  have  the  form — 

(i.)     113  :  355  •:  56.5  :  177-5 
and 

(2.)  56.5x*°=mn»:  177.5x10=1775-  360:1130+. 

In  the  3550  bckahs,  whence  the  1775  skekels,  we  have  cir- 
cumference to  1130-f-  ;  which  last  is  circumference  to  360, 
the  standard  year  or  Jehovah  year  value,  as  a  perfect  cir- 
cular element.  Here,  in  (2.),  we  have  the  form  of  the 
1 775'  or  hooks  of  the  -pillars  of  the  house  of  ychovah,  di- 
rectly connected  with  Jehovah,  in  the  form  56.5  X  i**  = 
mUS  where  Jehovah  is  shown  to  he  the  diameter  to  this 
very  1775  ^-^  <^  circumference :  so,  in  fact,  the  Jehovah  value 
is  being  raised,  in  -pari  ^assu,  with  the  1775  shekel  value 
of  the  hooks  of  the  -pillars.  In  heathen  mythology,  the 
hooks  of  the  pillars  may  have  indicated  the  hooks  binding 
together  the  opening  of  the  sistrum,  sacred  to  Isis,  or  the 
woman  ;  and  this,  as  the  Garden  of  Eden,  was  the  womb 
of  time,  virgin,  because  it  was  productive  of  itself.  The 
origin  of  measures,  however,  was  also  a  Jehovah  expres- 
sion, as  10,  or  picture  of  a  circle,  with  its  diameter  straight 
line,  the  perfect  or  straight  line  one,  hermaphrodite,  and 
of  the  perfect  circular  value  20612,  the  source  and  begetter 
of  all  things,  the  infinitely  small,  but  of  the  same  realizable 
proportional  value  as  i — 20612,  invisible,  intangible,  yet 
resident  at  the  meeting  of  the  male  and  female  cubes,  over 
the  ark,  and  between  the  cherubims.  As  the  7th  day  was 
the  kodcshed  day,  the  pure  virgin  day  or  circle,  so  also, 
when  the  tabernacle  was  completed,  as  a  badge  of  all  its 
containment,  the  high  priest  wore  on  his  forehead  a  plate 
of  pure  gold,  bearing  the  inscription 

where  the  same  feminine  trait  as  of  the  7th  day  is  predicated 
of  the  great  word.  Kodesh  VJchovah  was  holiness  to  the 
Lord.  By  the  various  hieroglyphic  powers  of  this  combi- 
nation, the  various  purposes  of  the  tabernacle,  for  measure^ 
sacrifice,  and  worship,  are  to  be  found  indicated. 

(a.)     There  is  one  fact  in  regard  to  Moses  and  his  works 


§  95-  Appendix  VI.  271 

too  important  to  be  omitted.  When  he  is  instructed  by  the 
Lord  as  to  his  mission,  the  foiver  name  assumed  by  the 
Deity  is,  I  am  that  I  am,  the  Hebrew  words  being 

a  various  reading  of  ^'^^T^    Now,  Moses  is  HC^D,  and  equals 

345- 
Add  the  values  of  the  new  form  of  the  name  Jehovah, 

21  -{-  501  +  21  =  543,  or  by  the  reverse  reading  345  ;  thus 
showing  Moses  to  be  a  form  of  Jehovah  in  this  combina- 
tion. 21  -T-  2  =  105,  or,  reversed,  501,  so  that  the  asher 
or  the  that  in  lam-that-Iam  is  simply  a  guide  to  a  use  of 
21  or  7X3-  501^=  251  +  ,  a  very  valuable  pyramid  num- 
ber, indicating  the  distance  from  the  intersection  of  the 
passage-ways  to  the  central  axial  line  of  the  structure. 
The  analysis  of  this  form  really  conducts  one  back,  by  ref- 
erence, to  the  Garden  of  Eden  form,  on  which  the  pyramid 
resulted.  Very  frequently,  however,  the  simplest  form  of 
symbol  use  is  the  most  important.  Bend  345  into  a  circle, 
and  we  can  read  354,  which  is  the  result  of  Bnosh,  as 
C^"IJ{<,  or  365  —  I  ==  364,  which  has  for  the  other  extreme 
■3^ t  —  I  =  354,  where  364  comes  from  the  kodeshcd  use  of 
the  7th  day,  as  7  X  4  =  28,  and  28  X  13.  or  52  x  7>=  3^4  ; 
thus  showing  Kodesh  V  Jehovah  truly  enough  !  And, 
again,  it  can  be  read  435,  and  435^2=217+,  or  the 
heel  use. 


272  Appendix  VII.  §  96. 


APPENDIX  VII. 

The  Fourth  Chapter  of  Genesis. 

§  96.     The  attempt  at  guiding  one's  way  through  one  set 
or  kind  of  hieroglyphic  readings  spurs  out,  here  and  there, 
hints  which  may  be  used  as  helps  to  other  kinds  of  con- 
struction.    Rabbinically  and  kabbalistically,  it  is  averred 
that  the  entire  Biblical  knowledge  is  held  in  the  first  four 
chapters  of  Genesis  ;  but  it  is  also  taught  that  the  subtlety 
of  teaching,  or  its  comprehensiveness,  is  such  as  to  prevent 
recognition  in  many  ways  and  details.     One  great  cloak  to 
blind  as  to  determined  readings  of  the  narrative  style  is  in 
the  making  use  of  the   hermaphrodite  condition  ;   for  in- 
stance, a  personification  combining  the  idea  of  male  and 
female  may  be  treated  of  as  -di  feminine  quality^  through 
determinative   construction,  while  at  the  same  time  it  may 
be  characterized  by  superficial  description  in  its  other  quality 
as  male.     Thus  the  name  Jacob,  ^pl^"%  or  J^i^^  is  heel,  is 
hermaphrodite,   where,   as    regards    the   whole    concreted 
name,  Jah  (or  Jehovah)  is  masculine,  while  heel  is  the  fem- 
inine part.     Jacob  evinces  this  by  seizing  with  his  hand 
(1»  :^  I  _|_4  —  5)  the  heel  of  his  brother.     The  word  T,  or 
hand,  has  a  sexual  meaning  masculine,  while  the  heel  is 
feminine,  and  yet  as  a  pictured  hieroglyph,  and  as  5,  it  is 
the  womb,  a  creative  number.     Thus  a  double  combination 
of  Jacob's  hand,  male,  with  Esau's  heel,  female  ;  or  of  Esau, 
male,  with  Jacob,  in  his  feminine  quality  oi  heel,  as  female, 
which  betokened  the  changes  of  relationship  which  they 
should  take  to  each  other  on  the  celestial  circle.     So  also 
with  relation  to  the  glyphs  of  Sodom.     Nork  shows,  clearly 
enough,  that  the  controlling  characteristics  of  the  Sodom 
description  are  feminine.     Its  geographical  location  was  at 
the  salt  lake,  and  Venus  sprang  from  the  salt  foam.     It  was 
the  as^haltum  or  bitumen  lake, — to  that  extent  a  Typhonic 


§  96.  Appendix  VII.  273 

emblem  of  darkness^  or  the  pit, — also  feminine.  It  was  at 
evening,  when  the  angels  went  over  from  Abram,  the  sun 
measure  (who,  as  typifying  this  measure,  was  at  midday 
seated  in  the  door  of  a  pyramidal  structure,  under  the  ver- 
tical rays),  to  his  brother,  or  countermart  (or  sister),  Lot, 
seated  in  the  gate  of  a  fortress^— 2\\  feminine  traits.  The 
recondite  meaning  connected  with  the  place  was  as  of  the 
abyss,  ecclesiastically  paralleled  to  woman^s  desire;  and 
thus  "  those^^  (men?)  of  Sodom  who  attempted  to  seize  the 
male  guests  of  the  patriarch's  brother,  though  his  daughters 
were  offered  a"5«^r-fice,  are  clearly  enough  determinative 
of  the  real  natural  fact  that  they  {'■'■  those^^)  were  women. 
Further  determinations  are  made.  It  is  Lot's  wife  that 
turns  back  with  longing  desire,  and  is  converted  into  a 
pillar  of  salt,  a  monument  of  combination  ;  while  it  is 
Lot's  daughters  to  whom  the  impulse  of  repeopling  the 
world  is  given.  The  tracing  of  the  subtle  substitutive  in- 
volutions of  these  qualities  becomes  the  necessity  for  the 
reading  of  the  more  important  teachings  of  the  esoterism. 
It  is  under  just  such  a  cloak  that  the  feminine  character  of 
Hebcl,  or  Abel,  is  concealed  in  4th  Genesis. 

It  has  been  seen  that  the  Garden  rested  on  the  Adam  or 
144  form,  as  4  squares  of  6  X  6  =  36  each,  around  a  central 
point ;  then  the  crossed  lines  are  extended  out,  so  that  the 
area  36  is  expressed  in  line  measure  of  that  number  ;  which 
36  is  diameter  to  113  o-f- ;  which  brings  up  the  113  :  355, 
from  whence  the  woman  and  the  Parker  numbers,  con- 
structive of  the  pyramid.  Now,  subdivide  these  lines  of 
36  by  4,  or  36  X  4  =  144  each,  and  in  number  we  have  4 
of  them.  The  operation  is  indicated  by  4^,  or  36  X  16  = 
576,  as  144  X  4,  and  the  letters  of  Cam's  name,  pp,  added 
as  to  their  full  values,  gives  the  character  value  of  16,  as 
100+  10 -{-50=  16 — o.  The  Garden  has  now  become, 
under  this  use,  one  of  a  square  of  144  in  the  center,  or 
Adam,  expanded  into  four  such  squares,  or,  together,  a 
large  square  of  144  X  2  =  288  to  the  side  ;  or,  ctibcd,  the 
Adam  or  hermaphrodite  cube,  as  a  primal  one,  is,  in  sep- 
arating into  male  and  female,  each  a  perfect  one,  enlarged 


274  Appendix  VIL  §  96. 

by  8  other  cubes  into  another  perfect  one,  where,  however, 
it  is  composed  of  the  separated  unities.  The  circumfer- 
ence of  this  large  square  is  144  X  2  —  288  to  the  side,  and 
288X4=1152  for  circumference,  and  as  indicating  this 
we  have  the  first  values  115,  by  reading  the  letter  values 
of  Cain's  name,  as  they  run,  in  ^p,  or  115.  The  measure 
of  a  horizontal  line  passing  through  this  garden,  then,  will 
be  noted  from  verge  to  center,  as  144 — 441  ;  counter  farted  ^ 
so  as  to  exhibit  separated  qualities,  just  as  it  was  in  the  ex- 
pression of  woman-man,  as  311 — 113;  and  this  is  the 
meaning,  or  source  of  meaning,  of  the  kabbalistic  use  of 
reverse  readings.  It  was  always  the  double  cube — i.  e., 
male-female,  i.  e.,  white-black;  and  it  explains  the  read- 
ing given  of  1656 — 6561,  or  6561 — 1656,  already  had.  But 
a  most  interesting  feature  now  presents  itself  in  this  subdi- 
vided value  of  this  garden.  144  is  12  X  12,  and  the  side 
of  the  great  square  of  144 — 441  is  12-J-12,  or  24  in  length, 
where  144  is  taken  as,  say,  inches,  and  reduced  to  feet. 
24  is  four  sixes,  or  6  X  4  =  24.  Now,  this  is  exactly  the 
measure  of  the  base  of  the  great  pj^ramid  in  this  identical 
scale  of  measure ;  for  i^o.^S^-\-feet,  which  is  diameter  to 

I 
a  circumference  of  600  feet,  is  numerically  just  -  of  the 

side  of  the  base  of  that  structure,  and  600  X  4  =  i\oofc€t, 
as  the  circumference  to  the  base  side  in  feet,  taken  as  a 
diameter  value. 

(Perhaps  a  simpler  way  of  explaining  the  likeness  is  this  :  The 
pyramid  base  side"  is  diameter  to  a  circumference  of  2^00  feet, 
which  can  be  used  as  its  equivalent ;  and  24  feet  is  the  charac- 
teristic of  this  base  side.  2^  feet  is  28S  itiches,  or  144  X  2.  144 
is  Adam,  the  nucleus  of  the  garden,  and  may  be  taken  as  the 
square  of  12,  for  area,  or  as  144  for  the  side  of  a  square.  Place 
this  in  the  center  of  four  squares  of  like  size,  and  the  side  of  the 
larger  square,  so  framed,  will  be  288,  or  the  characteristic  of  the 
base  side  of  the  pyramid  in  inches.  288  X  4  =  1152,  the  total 
circumference.  Besides  this,  this  1152,  as  designative  of  this  cir- 
cumference, is  symbolized  by  the  letters  INRI,'standing  for  earth, 
air,  fire,  and  water,  the  elements  composing  the  cosmos  which 
the  pyramid  measures.     Bend  these  letters  into  a  circle,  and  their 


§  96.  Appendix  VII.  275 

number  values  read  1152.     This  is  referred  to  in  the  last  part  of 
this  Appendix.) 

Here  the  characteristic  value  is  taken  in  24  feet.  Again, 
referring  to  the  garden  form  of  the  crossed  lines  being 
36 — 6^,  these  indicate  113 — 311,  for  113.0+  is  circumference 
to  2^  as  a  diameter ;  and  113  X  5,  if  this  be  so  subdivided, 
equals  565,  or  JllH,  or  Eva,  or  hovah.  But  to  indicate  the 
cube  of  8,  enlarged  from  the  cube  of  one,  the  letters  H  and 
n  are,  together,  an  oblong  of  two  squares  (p.  160),  or  the 
Phcnician  fence ^  giving  these  two  letters — viz.,  divided — 
and  one  part  of  this  oblong  is  H,  and  the  other  H  ;  but  H  is 
the  womb  letter,  or  5,  as  showing  the  half  of  the  -primal 
one,  and  taken  as  the  single  cube,  it  requires  just  8  others 
for  the  enlarged  cube,  and  the  letter  11,  the  other  part  of  the 
oblong,  is  8.  Therefore,  mil,  or  primal  Eve,  and  Hin,  or 
Eve  separated  to  be  the  -prodiici^ig  mother,  are  simply  de- 
terminative of  this,  as  the  one  is  H  (or  5),  Eve,  and  the 
other  n  (or  8),  Eve.  This  enlargement  is  based  on  the 
idea  that  for  every  perfect  woman  there  must  be  a  perfect 
man  ;  hence  the  combination  is  a  black  cube  and  a  white 
cube,  the  practical  value  being  in  the  meeting  of  the  cubes 
or  covenant:  so  that  while  (H)-ouva,  or  !lXi^)>  is  woman, 
(Ch)-ouva,  or  nXn)»  is  woman  having  a  husband.  But 
this  doubled  form  is  an  oblong,  and,  to  make  it  a  perfect 
square,  four  must  be  taken,  or  8  such  alternating  cubes,  to 
make  another  perfect  cube.  The  commingling  of  Adam 
with  Eve  produced  the  welding  together  of  the  two  Garden 
forms  in  Cain,  or  yehuvah,  who  was  the  divider,  or  meas- 
urer, or  distributor.  Cain  was  Vulcain,  and  Vulcain, 
with  the  Egyptians,  was  the  greatest  of  the  gods,  or  of  the 
Cabirim.  Vulcain  was  Pater-Sadic,  the  Right  One,  or  the 
Just  One  ;  and  by  Fuerst :  "  Sanconiathon  calls  one  of  the 
constellations  Mizor,  1?/D,  a  brother  of  Sadie,  pH^  (same 
with  Melchi-Sadic,  the  Just  One) — i.  e.,  Jupiter;"  which 
simply  shows  that  Mitsar,  or  Mitzar,  ll^'D,  Egypt,  was  the 
same  with  Mizar,  1?0,  and  was  both  wife  and  sister  of 
Jupiter,  who  was  the  Melchizadik  of  the  Hebrews. 
SeyfFarth,  Part  2,  p.  74,  gives  Cabiri?n  as  Gibborim,  "the 


276  Appendix  VII.  §  96. 

mighty  men  of  renown  in  those  days,"  in  6th  Genesis. 
And  Fuerst  says  of  the  Cabirim  (planets)  :  "A  name  of 
the  7  sons  of  pH^*,"  or  Pater  Sadie,  or  Cain,  or  Jupiter. 
As  the  expression  '■'-Adam  (144)  knew  Eve  (56-5  or 
56-8),  is  but  the  commingling  of  the  Garden  of  Eden  ele- 
ments, and  as  the  Cain  form  is  but  another  use  of  the  same 
elements,  it  is  most  interesting  to  read  the  teaching  of 
Irenaeus  (xxxiv)  (Adam  and  Cain  being  one),  that  "the 
father  and  the  son  lie  with  the  woman ^  whom  they  call 
Mother  of  all  that  live  (Eva)."  (Sod.,  p.  74.)  How  true 
it  is  here,  for  it  is  the  intermingling  of  the  squared  forms 
of  earth  measure  (Adam-Cain)  with  the  circular  measures 
taking  their  rise  from  the  woman  (HJJ^Nn,  5315)  ;  whence 
Eve,  as  shown. 

Before  proceeding  to  the  reading  of  4th  Genesis,  a 
governing  determinative  should  be  taken  into  considera- 
tion. Cain  has,  in  one  respect,  the  same  quality  with 
Adam — viz.,  he  is  "  <z  divider  of  the  Adam-h^''  or  tiller  of 
the  soil,"  and  as  with  Adam,  it  may  go  to  show  the  use  of 
measures  in  right  lines,  though  connected  with  circular 
values.  This  seems  to  be  determined  bv  the  fact  that 
Cain  is  said  to  be  "Jehovah;  and  the  other  fact  that  in  all 
the  conversations  in  this  glyph,  the  god-name  Elohim  (or 
31415),  circumference  value  is  dropped,  and  Jehovah^ 
mn*  (or  113  X  .5  =  56-5  X  ' "  (=  nin*)  =  565 >  Eva),  a  di- 
ameter value  is  alone  used.  Such  being  the  main  idea 
(whatever  the  uses  under  it,  which  no  doubt  involve  time 
and  earth  measures),  when  this  special  phase  of  the  problem 
is  worked  out,  and  perfectly  ended  in  the  Cain  glyph,  as  a 
variation  on  the  general  workings  of  the  main  problem,  the 
subject  is  resumed  under  the  other  form  ;  for,  as  determina- 
tive of  this,  the  TVsTV  form  is  dropped,  and  that  of  circum- 
ference is  again  taken  up  in  the  expression  "  for  God  hath 
appointed  me  another  seed  instead  of  Abel,"  where,  lor  the 
first  and  only  time  in  these  connections,  the  term  Elohim 
(31415),  God,  is  used.  The  seed  was  TW,  Seth,  the  year, 
ts  values  being  3  X  4  =  12,  and,  as  an  origin,  34-4  =  7. 

(a.)     (i.)  The  first  sentence  in  4  Gen.  i,  is  :  "And  Adam 


§  96.  Appendix  VII.  277 

knew  Eve,  his  wife  ;  and  she  conceived  and  bare  Cain,  and 
said,  I  have  gotten  a  man  from  the  Lord,"  agreeably  to  the 
accepted  translation,  which  is  manifestly  a  false  rendering. 
A  better  and  more  literal  rendering  is  :  "And  Adam  knew 
Eve  his  wife ;  and  she  conceived  and  bare  Cain,  and  said, 
I  have  measured  a  man,  even  ychovak."  The  reading  is 
ka'nithi  aish  eth  Jehovah ^  or 

Here  the  proper  name  is  taken  as  a  measure.  Wordsworth, 
in  a  note  on  4  Gen.  i,  on  this  passage,  says  : 

"  Cain — I  have  gotten\ — Katn,  from  Ka'nithi.,  I  have  gotten. 
Here  is  an  instance  of  the  principle  on  which  names  were  given 
in  primitive  times  — namely,  a  desire  to  indicate  some  leading 
characteristic  of  the  person,  or  thing,  to  which  they  were  given. 
See  (Genesis)  ch.  iii.,  v.  20.  Kain  intimates  acquisition.,  and 
Eve's  next  son  was  called  by  her  Abel — i.  e.,  vanity.,  'weakness'^ 

This  principle,  as  laid  down  by  Dr.  Wordsworth,  is  found 
everywhere  to  be  a  right  one.  Here,  while  the  name  may 
stand  for  a  great  variety  of  uses  (a  phenomenon  of  the 
hieroglyphic),  one  fundamental  recognition  is  oi  the  fact 
denoted  b}'-  the  act  of  Eve — viz.,  /  have  measured^  is  fol- 
lowed by  the  substantive  form,  a  measure,  or  Cain,  or  ye- 
hovah.  The  word  of  the  text  is  derived  by  Wordsworth 
from  ka'nithi,  I  have  gotten.  The  derivation  is  good,  for 
the  verbal  is  kanah,  HJp.  We  find  this  as  H^p,  a  substan- 
tive, meaning  measuring  stick,  or  rod,  the  beam  of  a  bal- 
ance, from  the  verbal  HJp  of  Wordsworth,  which  is  "iden- 
tical in  its  organic  root  with  IIJD,  or  Cdndh,  to  divide, 
separate.''  (Fuerst.)  So,  also.  Sir  William  Drummond 
takes  the  same  derivation — viz.,  as  a  measure.  (Qidipus 
Judaicus,  p.  196,  on  chap.  15,  v.  22,  and  chap.  17,  v.  9, 
of  the  Book  of  Joshua.)  The  derivations  run  off  into  other 
significations  ;  as,  for  instance,  H^D,  Cdndh,  to  divide,  sep- 
arate, is  same  as  11^11,  chdndh,  both  meaning  to  fierce,  as 
"  n^n,  chdndh,  (i.)  to  incline,  to  bend  ;  (2.)  to  fierce  of  a 
tueapon,  organic  root  of  which  T\'T\,  chn-h,  also  lies  in  |p, 
Kn  (pp,  Kan),  belonging  to  pp,  Kay  in,  Cain  (proper 
name)."     (Fuerst.)     As  exceedingly  pertinent  to  this  sub- 


278  Appendix  VII.  §  96. 

ject,  after  HJH,  chdndh,  and  next  in  order  of  words  comes 
the  word  "  111^11,  chanoch,  noun  proper,  (i.)  of  the  son  of 
Cain  (meaning  Instructor,  Initiator),  by  LXX,  e'vw;^,  (2.) 
of  the  son  of  Methuselah,  who  founded  the  365  year." 
(Fuerst.)  It  is  so  pertinent,  because  of  showing  Cain  to 
be  the  measure,  in  Chanoch  his  son,  the  instructor,  or  ini- 
tiator, of  the  astronomical  circle  and  the  solar  year.  And 
also,  likewise,  "  The  god  of  //;«e  was  worshiped  under  the 
names  of  pfl,  chiun,  by  the  Egyptians  ;  clearly  taken  from 
p3,  ciun'^  (Fuerst,  under  pD,  ciun,  a  name  of  Saturn,  or 
Seth) ;  and  V\'2,  diun,  is  same  with  pp,  Cain.  Th^  pillar 
was  a  mark  of  the  year,  and  Nork  says  of  Cain  that  he 
was  as  the  German  pfeil,  pfcilcr,  spear,  ox  -pillar,  or  the 
god  with  the  hasta  or  spear  point.  Thus  one  has  the  word 
Cain  as  a  dividing,  splitting,  ox  piercing  measure  of  time ; 
and,  besides,  he  was  the  earth  measurer.  Now,  Vulcain 
was  the  Pater  Sadie,  or  Melchizadik,  and  as  a  form  of 
Mars,  with  the  Egyptians,  he  held  the  ecliptic.  Libra,  or 
the  balance,  and  also  was  the  piercer,  with  the  sign  of 
Mars,  or  the  hasta,  or  spear.  Tubal-Cain,  son  of  Cain, 
has  been  taken  by  commentators  as  Vulcain,  but  there  was 
no  need  of  going  so  far  for  the  sameness.  The  very  name 
Vulcain  appears  in  the  reading,  for  in  the  first  words  of  4 
Gen.  5,  is  to  be  found  V'elcain,  or  Vulcain,  agreeably  to 
the  deepened  u  sound  of  the  letter  vau.  Out  of  its  imme- 
diate context,  it  may  be  read  as,  "  aiid  the  god  Cain,'^  or 
Vulcain.  If,  however,  anything  is  wanting  to  confirm  the 
Cain-Vulcain  idea,  Fuerst  says :  "  Pp?  Cain,  the  iron 
point  of  a  lance,  a  smith  (blacksmith),  inventor  of  sharp 
iron  tools  and  smith  work."  Cain,  as  a  number  value,  is, 
as  the  letters  run,  115;  adding  the  full  values  160,  or 
character  value  of  16,  or  adding  the  character  values  (as 
I  -|-  I  -f  5)  is  7.  He  is  at  the  head  of  a  system  of  calcula- 
tion, PS  Seth  is ;  Seth,  TS^,  being  3 — 4,  as  the  letters  run, 
adding  the  character  values,  is  7,  or  multiplying  them, 
3  X  4=12.  But  Seth  seems  to  be  the  more  perfect  value, 
for  it  is  composed  of  the  productive  numbers  3  and  4. 
Mars  and  Vulcain,  or  Cain,  or  Pater  Sadie,  are  forms  of 


§  96.  Appendix  VII.  279 

each  other.  Under  the  Egyptian  forms  of  the  celestial 
system,  by  one  or  other  form,  Mars  held  the  solstice  and 
equinox  points.  But  Mars  was  the  generator.^  while  Vul- 
cain  was  the  divider  or  measurer. 

(2.)  Cain,  as  son  of  Adam,  144,  was  Adam  ;  and,  as 
son  of  the  woman^  he  was  113,  man;  and  113  X. 5  = 
56.5  X  ' "  (=  XVSXV)  =  565  =  mn  =  Eva  ;  where,  in  56.5 
X  ^^,  Jehovah  springs  from  113,  ox  man:  so,  thus  Cain, 
the  measure^  was  man,  as  113,  and  Jehovah  as  565*. 
And  so,  also,  Cain  thus  welding  together  the  Adam  and 
woman  forms  of  the  garden,  thus  becomes  really  a 
determinative  of  what  has  preceded  in  the  narrative. 
He  was  144,  and  its  feminine,  or  circular  derivatives  ;  and 
this  is  determined,  for  it  is  said  "Cain  was  a  divider  (by 
measure)  of  the  earth."  The  words  are  rTD"1N  ID^,  obed 
Adam-h.  The  verbal  obed,  is  to  divide,  to  separate,  to 
mark  by  long  stripes  or  furrows  ;  and  these  are  the  more 
radical  meanings,  the  secondary  derivation  being  to  till,  to 
cultivate.  It  is  thus  expressly  said  that  Cain  is  a  divider 
of  the  Adam-h,  or  of  the  144-5,  or  720.  Taken  literally, 
and  always  in  division  keeping  the  counterpart  form,  the 
divisions  of  the  square  would  be  720  -^  2  =  360 — 063  ;  360 
-^  2  =  180 — 081  ;  180-^  2  =90 — 09  ;  where  the  division  has 
come  to  its  lowest  integral  terms  in  the  square  of  3.  But, 
virtually,  it  is  seen  that  this  is  but  the  Garden  form.  It  is 
very  curious  that  the  counterpart  values  present  strange 
co-ordinations  with  the  general  subject-matter ;  for,  6-;^,  = 
9X7,  and  7  is  characteristic  of  ^,  and  9  is  of  >^,  or  together 
^^,  ots,  the  tree  of  the  Garden;  81  is  the  side  of  the  area 
square  of  6561,  the  Parker  base;  while  9,  the  last  sub- 
division, with  the  16  of  Cain's  name,  gives  9  X  16  =  144, 
or  a  curious  restoration  of  the  Adam  form  of  144  in  its  sub- 
division of  the  cube  of  3,  and  the  square  ot  4  ;  and  16  -^  9 
=  1777.77+,  the  cubit  value  of  the  base  of  the  pyramid. 
Cain's  function  seems  to  be  marked  as  of  the  quadrant  di- 
vision lines  of  the  square,  or  of  the  cube,  or  he  seems  to 
represent  the  cross  division  lines.  It  has  been  shown  that 
for  calendar  purposes,  Cain,  as  115,  was  the  complement 


28o  Appendix  VII.  §  96. 

lo  make  up  the  standard  year  of  360  days,  or  the  celestial 
circle  of  360  degrees,  as  28  +  217  -|-  115  =  360  :  and  that 
on  this,  as  a  standard,  the   addition   of  the  5   epagomenai 
days  made  up  the  full  solar  year  of  365  days.     Thus,  Cain 
can  be  taken   as  this  value   of  360   degrees,  of  which   he 
holds  the  crossed  lines  as  exactly  balanced,  because  he  was 
the  yust  One.     This  was  the  standard  celestial   circle,  of 
which  the  horizontal  diameter  was  the  ecliptic,  to  which 
plane  all  movements  of  the  heavenly  bodies  were  referred. 
The  divisions  of  the  Zodiac  (ring  of  life)  were  laid  off  on 
this  circle  in  12  compartments.     The  compartment  of  Sag- 
gitarius  bounded  on  the   winter  solstice,  and  was   called 
Tohi  as   a  month;    then   followed  the   Goat,  Waterman, 
Pisces,  Aries,  Taurus,  and  Gemini,  six  divisions  closing 
up  to  the  summer  solstice  in  Gemini,  which  was  called  Pani. 
But  by  this  distribution  Scorpio  falls  to  the  second  sign  be- 
low the  autumnal  equinox.     The  actual  distribution  of  the 
full  solar  year  months,  on  these  signs,  did  not  accord  with 
them  ;  but  June  being  Cancer,  as  a  month,  to  accord  with 
the  signs,  fell  back  on  to  the  sign  Gemini,  of  the  standard 
circle  or  zodiac,  22  degrees,  or  days,  so  that  June  22,  for 
the  month,  accorded  with  the  boundary  line  of  Pani.     By 
this  arrangement,  which  was  the  correct  one,  Scorpio  would 
also  fall  back,  as  a   month,  to  within   ten   degrees  or  days 
of  the  boundary  line  of  the  autumnal  equinox  (September 
22  to  end  of  month  inclusive  9  days  -\-  the  ist  day  of  Oc- 
tober) ;  which  ten  degrees,  or  ten  days,  was  the  amount  to 
be  added  to  the  355  year,  or  Abram-Isaacyear,  to  make  up 
the  full  complement  of  365  days.     Putting  these  ten  days 
in  a  box,  carried  the  last  day  of  the  355-day  year  over  this 
gap  of  ten  degrees,  which,  as  blotted  out,  carried  or  con- 
tinued the  equinoctial  to  the  first  day  of  Scorpio,  not  as  next 
to,  but  as  the  actual   first  day  of  October.     And,  indeed, 
this  was  the  adjustment  as  made  by  the  Hebrews  ;  for  355 
was  their  basic  year  value,  and  hy  Xheiv  squared /orm,  they 
followed  the  order  of  the  actual  months,  so  that  the  third 
quadrant  of  the  year  run  :  Leo,  Virgo  as  the  corner  square, 
and  then  Libra.     By  this  arrangement,  this  or  the  holy 


§  96.  Appendix  VII.  281 

square,  or  cube,  was  embraced,  between  Cancer  and  Scor- 
pio, depicted  as  so  much  alike  as  to  represent  the  cheru- 
bim, measuring  the  holy  cube  in  the  holy  of  holies.  It 
was  the  function  of  Cain,  to  adjust  these  unequal  qualities, 
the  one  to  the  other;  i.  A  standard  year  base;  2.  A 
standard  zodiacal  circle ;  3.  The  arrangement  of  the 
actual  year  of  365  daj's  for  distribution  on  this  circle.  But 
it  is  seen  that  under  the  squared  form  Scorpio  could  be 
treated  of  as  Libra  on  the  standard  circle,  so  that  the  same 
phraseology  would  apply  to  each.  By  this  month  arrange- 
ment, also,  the  same  figures  would  apply  to  the  same  sea- 
sons perpetually ;  while,  by  the  fixed  value  of  the  signs  of 
the  Zodiac,  they  would  fall  away  from  fixed  locations  of 
the  year  by  the  lapse  of  time,  as  they  have  done. 

Thus,  under  this  explanation,  one  of  these  cross  lines 
leads  from  Scorpio,  and  this  was  the  place  of  piercing  the 
dying  sun,  or  rather  of  impregnating  the  deaths  with  the 
new  sun.  Here,  at  the  autumnal  cross,  as  referred  to  the 
center  of  the  square,  was  the  piercing  of  Abel  accom- 
plished ;  but  unfortunately  for  what  is  called  orthodoxy, 
the  bloodshed  was  chdthan  ddnii,  *D"1  [riH,  or  the  bloods 
of  the  bride  chamber.  How  exceedingly  wonderful  the 
connecting  links  of  this  esoterism  are  !  Jesus  was  the  son 
of  man,  the  Ben  Enosh,  or  Enosh,  or  365  —  i  =  364,  the 
son  of  the  year,  or  Scth,  TW  ;  but  the  patriarch  Judah,  son 
of  Jacob,  the  Leo  or  lion  of  the  Zodiac,  and  renewer  of 
this  Garden  of  Eden  glyph,  in  his  ^hase  of  working,  found 
Tamar  on  the  same  crossed  lines,  at  the  same  place  (the 
solstice  line  crosses  the  equinoctial  at  the  center ;  the  cross- 
ing being  in  common,  Judah  looked  down  to  his  opposite 
for  Tamar,  and  met  her  in  the  center,  just  as  Scorpio  met 
Taurus  at  the  same  place),  but  at  harvest,  along  the  solstice 
line  between  Leo  and  the  goat,  and  she  was  the  ancestress 
of  Jesus  through  Pharez.  Now,  while  Enosh  is  the  j^ear, 
Tamar  was  the  palm-tree,  a  recognized  symbol  of  the  sun 
and  of  the  year,  in  its  hollowness,  or  nothingness,  showing 
another  phase  of  this  astronomical  picture  ;  so  that,  both 
by  numbers  and  by  types,  and  also  by  derivation,  Jes-us 


282  Appendix  VII.  §  96. 

was  the  sun,  as  well  as  a  man  ;  and  as  such,  Jesus  and  Abel 
were  one.  The  glyphs,  as  the  saying  is,  run  on  all  fours 
together.  Cain,  a  Mars  form,  pierces  Abel,  and  the  Roman 
soldier,  a  son  of  Mars,  pierces  Jesus.  Both,  by  Kabbal- 
ism,  are  pierced  at  the  meeting  of  the  cubes,  or  covenant, 
or  at  the  intersection  of  the  crossed  lines.  Abel  is  said  by 
some  to  be  the  same  with  Abelion,  the  sun.  In  the  "  Ros- 
icrucians,"  by  Hargrave  Jennings,  is  a  representation  of  the 
astrological-theological  cross.  The  man  Jesus  is  depicted 
as  half  male,  half  female  ;  the  female,  or  sinister,  or  dark, 
or  evil  side,  being  blackened.  On  this  cross  He  is  pierced 
in  the  sinister  side,  in  the  venter,  which  by  the  chart  is 
Virgo  (but  should  be  Virgo,  Scorpio),  the  place  of  piercing 
being  in  the  side  of  the  man,  or  in  the  approach  to  the  door 
of  Indranee,  and  just  where  the  woman  was  taken  from 
the  man's  side  in  the  Garden.  But  man,  as  311,  is  the 
woman,  or  the  two  are  interchangeable  under  the  coun- 
terpart form  311 — 113,  so  that  the  piercing  is  the  type  of 
the  consummation  of  marriage,  duplicated  in  that  oj"  the 
rite  of  circumcision. 

So  Cain  is  Melchizadik,  or  Pater  Sadie,  or  Jupiter  ;  the 
Just  One,  or  the  Right  One,  or  the  Adjuster.  He  is  the 
ecliptic,  and  the  balance  line  for  equinox,  and  solstice.  He 
is  the  divided  cube,  representing,  as  to  one  of  its  phases, 
the  heavenly  measures.  It  is  not  a  single  cube,  but  is  made 
up  of  8  cubes  of  144,  each,  in  its  subdivided  form,  com- 
bining distinct  males  and  females,  for  production. 

(3.)  The  narrative  proceeds,  "And  she  again  bare  his 
brother  Abel ;"  where  the  word  brother  is  simply  an  ob- 
scuration of  the  sex  of  Abel  (he  being  hermaphrodite), 
which  in  reality  predominates  in  this  glyph  as  /c?nale.  It 
is  observable,  too,  that  no  mention  is  made  in  this  case  of 
knowledge  by  Adam.  It  is  so  in  the  first  verse,  and  it  is  so 
in  the  close,  as  relates  to  Seth,  but  here  there  is  omis- 
sion. Abel  is  7^,T  Hebel,  and,  adding  the  character 
values  (3+2  +  5)  equals  10,  or  the  perfect  one,  or  Jeho- 
vah, showing  that  Abel  and  Cain  are  but  phases  of  the 
same  form — viz.,  of  Jehovah.     As  this   is   so,  while  ^^,-1, 


§  96.  Appendix  VII.  283 

Jlcbcl,  has  its  significant  use  as  a  single  word,  it  is  suscep- 
tible to  division  into   ^DTF,  or  H-Bl,  or  Thc-Bcl,  or  the 
sun.     In  this  form  the  values  run  32-5,  and  32  X  5  =160  = 
Cain ;  thus  showing  the  collateral  sameness.     As  a  num- 
ber value  10  is  the  perfect  cube  (so  was  Cain)  ;  it  is  also 
circumference  to  31.8  as  a  diameter,  and  this  was  the  Gnos- 
tic Christ,  who  was  Jehovah.     But  the  double  form  of  Je- 
hovah, as  male-female,  is  here  eliminated,  because  by  the 
determinatives  Hebel  is  made  to  assume  the  feminine  side 
of  his  own  form  exclusivel3^     The  meaning  of  the  word 
Hebel  is  emptiness,  nothingness.     This  is  the  idea  of  the 
primal  God.     In  Kabbala,  the  first  cause^  God,  is  named 
rj<,  oin,  nothing.    (Franck,  115,  quoted  from  Sod.  p.  67.) 
Nothingness  is  used  as  a  mark  of  the  female.     Nork  says 
that  the  beautiful  Naamah  was  an   astronomical   name   for 
Venus  ;  as  she  was,  also,  he  says,  the  Bohu,  or  word  for 
void  in  i  Gen.  v.  2.     Take  other  words  of  like   and   kin- 
dred and  correlative  meanings  :  p^^  ayin  —  "8 
from  p^,  un  (==p5<,  un),  same   as  pi<,  aven,  nothingness, 
vanity  (=7]3rT'  ^^^^)?  sin,  lie,     .      .      .     but  see  p^,  o;z." 
(Fuerst.)     Under  p^,  on,  but  in  form  p|^,  avon,  is"  found 
the  idea  of  emptiness,  with  sin  and  cohabitation  all  com- 
bined.    This  is  determinative  of  the  cha7-acter  oi\h^  circle 
as  a  personage  :  (i.)  That  it  is  but  the  circle  part  of  the  10, 
the  straight  line,  or  diameter  value,  being  left  out — i.  e.,  it 
is  an  empty  circle  ;   (2.)  That,   sexually,  Abel  is  feminine, 
for  the  purpose  of  this   glyph.     This   is   again  determined 
with  a  new  significance  in  the  description,  "And  Abel  was 
a  keeper  of  sheep,"  or   follower  of   cattle.      The  words 
keeper   of  sheep,   are   jj^l^.  Hyi,  roeh  tson.     This  word 
roch,  keeper,  is  a  compound  of  ^"1,  ra,  evil,  bad,  wicked, 
malignant — in  short,  the   early  church   characteristics  of 
woman;  and  with  appended  H,  h,  is  not  only  a  shepherd, 
but  a  shepherdess.     But  take  the  word  as  a  numerical  de- 
terminative, ^"1=  27,    n  =  5,   and  27X5=135,  or  .1:^*K, 
or  woman.     Again  under  p}<,  avon,  same  as  p^,  un  (vari 
ously  pointed),  not  only  are  the  same  meanings  expressed, 
but,  also,  it  is  used   as    On,  or  Heliopolis,  the  city  of  the 


284  Appendix  VII.  §  96. 

Sun^  which  is  the  hollow  circle  of  the  year.  But,  indeed, 
7^n  '  <^h^bcl,  signifies,  to  conceive^  2X^0  ^ains  of  birth. 

And  thus  a  feature  of  the  glyph  is  of  the  Garden  of 
Eden:  (i.)  In  its  masculine,  or  right  line,  form  of  Cain- 
Adam,  and  (2.)  in  \{s  feminine ,  or  sun  circle,  form  of  Abel ; 
and  its  object  is,  in  some  sort,  to  show  forth  astronomical 
applications  of  the  measuring  elements  of  one  to  the  other. 
But  as  Cain,  as  The  Right  One,  holds  the  balances,  or 
beams  of  the  balances,  and  there  are  two  balances — viz., 
that  of  the  equinoxes  and  that  of  the  solstices — he  as  di- 
vider, or  center  crossed  lines,  of  the  Adam-h,  cuts  this 
circle  in  its  quadrants.  It  has  been  shown  that  the  bal- 
ance opposes  birth  and  death  in  the  Mars  form.  The 
chief  points  were  in  Aries  and  Scorpio. 

Now,  there  is  a  curious  reflection.  In  Hebrew,  the  bal- 
ances are  D^JtK'D,  m-oznim,  while  the  cars  of  the  head  are 
D*J?{<,  oznijn,  the  precise  same  word,  save  the  mem,  D,  pre- 
fixed. The  type  is  clear  enough,  for  the  division  of  the 
head  at  the  ears  exhibits  this  very  glyph  of  the  Mars  form 
of  birth  and  death,  as  balanced  in  the  equinoctial  scales. 
To  join  the  two  symbols,  as  significant  the  one  of  the 
other,  in  the  Hindu  form,  over  the  mouth  of  the  vagina  is 
drawn  the  scull  and  crossed  bones,  forming  a  kind  of  mon- 


ogram   for   Ife.      In    church   emblems,    one   finds 


^ 


or  crossed  bones  with  this  letter  character,  which  is  the 
letter  p,  kopf,  or  symbol  of  the  half  of  the  head  back  of 
the  ears. 

(4.)  By  considering  the  place  of  Scorpio,  or  D'lilah,  in 
its  evil  aspect,  as  connected  with  its  feminine  quality,  then 
it  would  come  under  the  adjective  form  of  evil,  or  J^l,  ra  ; 
and  the  opposite  to  this  would  be  good,  or  y\r\,  tobi,  as 
designative  of  the  two  opposite  qualities.  Now,  by  the 
ancient  Egyptian  charts,  the  zodiac  sign  of  Saggitarius, 
bordering  on  the  winter  solstice,  carried  the  name  Tobi,  or 
the  Hebrew  'y\^,  good;  while  the  opposite  sign  of  Gemini, 
bordering  on  the  summer  solstice,  carried  the  name  Pani, 


§  96.  Appendix  VII.  285 

or  Hebrew  Pant,  ^J£3,  /ace  or  aspect.  The  astronomical 
course  of  going  from  Tobi,  by  way  of  the  vernal  equinox, 
which,  as  opposed  to  Scorpio,  was  ^ood,  to  the  summit,  or 
Pam\  would  be  upward  to  the  highest  point,  where  the 
aspect  or  face  of  the  year  would  change  to  its  reverse  de- 
clining. From  Panty  the  course  of  the  seasons  would  be 
declining,  by  way  of  Scorpio,  or  evil,  toward  the  winter 
solstice.  Now,  taking  what  is  said  to  be  so  as  to  the  offer- 
ings, Cain  being  yehovak  in  this  glyph,  as  a  diameter 
value,  or  as  diameter  values,  has  nothing  to  do  with  him- 
self,  but  does  in  his  masculine  capacity  shine  (for  the  word 
is  shine)  favorably  upon  the  circle  of  the  year,  or  zodiac, 
or  life;  or  upon  Eve,  Venus-Naamah.  At  the  summer 
solstice  point  is  the  intersection  of  the  diameter  line  with 
the  curve,  at  the  highest  reach  of  the  sun.  The  sun  here 
is  vertical,  just  as  at  the  noon  point,  and  the  standing  still 
of  the  sun  at  the  noon  point  was  called  *01,  ddjui,  by  the 
Vulgate,  and  LXX,  (Fuerst),  and  ddmi,  ^01,  is  exactly  the 
same  word  for  the  bloods  of  Abel,  which  Cain  shed.  Here 
was  the  fiercest  power  of  the  sun  looking  down  vertically 
along  the  solstice  line  to  the  intersection  of  the  cross  lines. 
At  the  same  time,  his  aspects  change  or  fall  to  his  declining. 
This  is  actually  described.  It  says  :  "And  it  burned  upon 
Cain,  and  his  aspect,  *J£3,  Pani,  changed  to  descending." 
Now  follows  a  description  of  where  the  sun  is  going  to  in 
descending,  by  a  history  of  his  travel.  The  words  are  : 
"  If  thou  doest  well  (good,  Tobi,y\\2i),  there  is  exaltation, 
rising'' — i.  e.,  you  will  rise  by  way  of  the  good  side  ;  "but 
if  thou  doest  not  well  (when  you  are  descending).  Sin 
(feminine  nj^DIl,  chattath)  is  a  Lier-in-wait  at  the  door  or 
opening  (or  Sin  is  at  the  qjiadrant  line,  at  the  opening ; 
for  YT\,  rbts,  the  Her  in  wait,  is  also  the  ^th  side,  as  of  a 
cube,  or  square,  as  well  as  a  cotich  to  lie  on.)  Again: 
"Sin  lieth  as  a  copulatrix,  at  the  door  or  opening; 
for  J*2"),  rhts,  is  same  with  '^*T\,  rba,  and  is  not  only  to  lie 
down,  to  cotich,  but  also  to  copulate.  The  word  for  open- 
ingis  in  the  same  kindof  connection,  for  piinfi,  piththachon, 
the  opening  of  the  mouth,  and  also  H^nnD,  fthach  vah. 


286  Appendix  VII.  §  96. 

or  "Jail  is  causer  to  bear,  where  El,  or  Jah,  is  conceived 
of  as  the  creative  world-power."  (Fuerst.)  In  other  words, 
"At  Scorpio  you  will  find  Naamah,  as  beautiful  as  wicked, 
who  is,  in  this  instance,  the  feminine  part  of  your  brother 
Abel."  And  now  comes  a  great  determinative,  fastening 
this  interpretation,  as  of  marriage,  or  the  consummation 
of  marriage.  In  the  i6th  verse  of  the  3d  chapter,  as  to  the 
woman,  it  says  :  "And  thy  desire  shall  be  to  thy  husband, 
and  he  shall  rule  over  thee,"  which  was  the  accompaniment 
of  sin,  or  transgression,  or  crossing,  as  a  quality  deter- 
mined upon  to  be  the  characteristic  of  woman  for  all  time. 
Here  (obscured  under  the  male-female  form)  it  is  said  as  to 
Hebel,  as  Sin,  to  the  man  Cain  or  Jehovah,  "And  her 
(his)  desire  shall  be  unto  thee,  and  thou  shalt  rule  over  her 
(him)."  This  seems  to  mark  out  an  unmistakable  character 
of  the  glyph.  But  it  is  followed  by  the  fact,  for  it  was  that 
they,  being  in  the  dividing  of  the  field  (rflC^"!!,  B-sadeJi), 
Cain,  the  rod,  rose  up  and  violated  his  brother.  It  was 
marriage,  and  the  bloods  that  were  shed  were  the  ^D1  [nH, 
chathan  ddmi,  or  bloods  of  the  bride  chamber;  and 
they  were  to  be  found  as  part  of  the  h-adam-h,  or  3600 — 
0063.  The  Cain  form  of  the  garden  was  144 — 441,  and 
the  bloods  shed  are  441,  or  ^D"T,  or  by  counterpart  441 — 144, 
which  simply  shows  that  these  bloods  were,  after  all,  but  a 
means  of  division  of  the  garden  for  astronomical  and  other 
purposes  ;  and  as  the  sun  standing  still  is  vertical,  as  coin- 
ciding with  the  one  Cain  division  line,  is  by  name  ^D1, 
ddmi,  or  441,  so  the  bloods  of  Abel,  shed  on  the  other,  and 
horizontal  division  line,  are  also  *D"T,  or  441.  Considering 
the  144 — 441  or  441 — 144  form  of  the  Garden,  and  the 
exact  fittingness  of  these  applications,  as  441  and  441,  for 
ddmi,  thus  twice  used,  respectively,  for  solstice  and  equinox 
line,  with  the  narrative  form  of  explanation,  and  the  inter- 
pretation of  the  glyph  for  this  phase  seems  good. 

(5.)  But  the  Cain  form  of  the  Garden,  144 — 441,  has 
been  shown  to  be  in  the  reduced  form,  exactly  significant 
of  the  base  of  the  great  pyramid — i.  e.,  144  inches  is  12,  say, 
feet,  and  12  =  6  +  6;  therefore,  there  being  144  X  2  to  the 


§  96.  Appendix  VII.  287 

side  of  the  Garden,  this  is,  in  this  reduced  form,  four  6s,  or 
6  X  4=  24  ;  and  indeed  the  actual  measure  of  the  side  of 
base  of  the  pyramid  is  diameter  to  a  circumference  of  24. 
Now,  since  from  the  very  first  line  of  Genesis,  through  the 
Garden  of  Eden  scene,  there  has  been  a  continuous  and 
systematic  reproduction  of  the  pyramid  elements  of  con- 
struction, in  another  mode  of  working  them,  with  also  the 
very  foundation  principles  and  numbers  on  which  it  was 
constructed,  to  be  found  both  in  the  Garden  and  in  the  flood 
glyph,  it  might  well  be  expected  that  this  4th  chapter,  like- 
wise, would  be  really  founded  on  the  same  method  as  the 
exactly  correct  one  laying  at  the  base  of  all  other  phases 
to  be  presented.    And,  indeed,  the  connecting  link  between 
the  general  construction  of  the  exterior  and  of  the  interior 
work  does  seem  to  exhibit  itself  as  obscurely  hidden  away. 
Cain  and  Abel  are  together  in  the  dividing  of  the  field. 
The  word  is  sddch,  TT]^,  field,  and  rather  means  a  dividing 
as  of  a  field.     With  this  word  is  the  prepositional  prefix  D, 
or  B  ;  or  the  whole  is  mtJ^  — D,  B — sadeh,  and  for  value 
we  find   the    character  values  as  they  run,  345-2,  which 
may  designate  the  counterpart  use  of  345 — 543.     Now  con- 
sider, however,  that  we  have  the  exact  terms  of  the  pyramid 
base  in  the  Cain  Garden  form,  as  shown,  and  then  that  we 
have  the  Hebel  circle  in  connection  with  it.     Then  here 
there  are  the  two  elements  necessary  for  ^putting  the  -pyra- 
mid ill  a  sphere.     Now,  refer  to  the  geometrical  problem 
for  the  construction  of  the  interior  works,  §  74.     One  por- 
tion of  this  problem — viz.,  that    having  reference   to  the 
great  salient  characteristics  of  the  interiorworks — is  founded 
on  "  circular  elements  three,''  as  given  in  §  82,  namely  : 

"(3-) 


Height, 

309.-}-  feet 

base  side, 

2 

243-+    " 

— base  diagonal, 

343-+    " 

(( 


Radius,  345-+ 

"These  are  the  circular  elements  whence  the  complete 


288  Appendix  VII.  §  96. 

pyramid,  as  to  its  inside  work,  is  fitly  framed  and  put  to- 
gether." 

Here  the  radius  value  is  given  at  345,  and  the  diameter 
value  would  be  345-2.  But  here  in  the  word  B-Sadch, 
T]1^*"2,  yve  have  345-2,  this  very  value.  Not  only  so,  but 
adding  the  full  values  of  the  letters  of  the  word  Sadck,  and 
we  have  t^,  300  -|-  1,  4  +  H,  5  =309,  which  is  j'usl  the 
height  of  \.h\s  ^pyramid  three,  as  shown.  Not  only  so,  but 
the  343,  gives  the  value  343  of  the  descending  passage- 
way. It  is  next  to  impossible  to  prevent  the  mind  being 
convinced  that  these  lines  of  similitude  are  intentional, 
where  the  various  corroborative  data  are  taken  into  bear- 
ing. But,  really,  in  connection  with  these  pyramid  coin- 
cidences, there  is  one  which  seems  absolutely  to  confinn 
or  establish  the  relation.  It  will  be  noticed  that  "  circular 
elements  three"  are  connected  with  the  problem  of  " /«- 
terior  geometrical  construction,'''  agreeably  to  the  diagram 
shown  in  §  74  {b).  Referring  to  that  diagram,  it  will  be 
seen  that  the  309.397+  referred  to  is  geometrically  con- 
nected with  that  angle.,  which  has  been  supposed  to  be  that 
of  the  roof  of  CampbclVs  chainbcr,  and  of  the  queen's 
chainbcr,  in  the  pyramid.  That  angle  has  been  shown  to  be 
115*^  (see  §  76).  Now  the  name  Cain,  or  pp,  equals,  tak- 
ing the  character  values  as  they  run,  115,  as  has  been  so 
often  referred  to.  Independently  of  this,  in  345  we  find 
the  name  Moses,  UtTQ,  =345,  used  as  /  am  that  I  am, 
shown  also  to  be  345,  in  the  Pharaoh  glyph.  So,  also, 
345  X  6=  217-0,  or  it  is  a  multiple  of  the  heel,  or  Jacob 
value  ;  while  if  345  be  bent  into  the  form  of  a  circle,  it  may 
be  read  354,  or  the  lunar  year  value.     Not  only  so,  but  in 

I  . 

the — base  side  of  these   designated  pyramid  elements — 

viz.,  in  the  value  243 — we  find  the  name  Abram.  More- 
over, in  this  connection,  it  has  been  shown  that  the  height 
of  the  intersection  of  the  floor  line  of  the  grand  gallery 
with  the  south  wall  thereof,  above  the  base  of  the  p3^ramid, 
was  diameter  to  a  circumference  of  5184,  the  solar  day 
value.     Well,  5184  =  72  X  72,  and  this  is  the   division  of 


§  96.  Appendix  VII.  289 

the  central  square  of  144  of  the  Cain  Garden,  or  144  -^  2 
=  72 — 27.  So,  indeed,  here  in  this  combination  is  Moses, 
Abram,  heel  or  Jacob,  with  Jehovah,  and  Christ ;  and  all 
are  developed  in  the  pyramid.  The  divided  form  of  this 
Jicld  would  take  the  numerical  display  of 

345— 543 » 
which  again  presents  strange  features;  for  543-^  7  =  63, 

and  63-H  7  =9.  But  7  and  9  are  the  characteristic  values 
of  VJ/,  or  <?/5,  the  tree  of  the  Garden,  the  twining  together 
of  the  two  parts  of  which  indicates  the  *D1  \T\T\,  chatha^i 
dami^  or  consummation  of  marriage,  in  its  attendant  blood- 
shedding.  So,  also,  7  X  7»  or  sevenfold,  seems  to  look 
toward  the  sevenfold  ot  Cain,  and  the  70  and  7  fold  of 
Lamech.  7  X  7^49,  the  perfect  square,  to  which  if  one 
be  added,  the  result  is  50 ;  and  is  the  subject  of  the  curious 
note  referred  to  in  Land  Marks  of  Freemasonry.  So,  345 
+  543  =  888,  and  somewhere  this  value  is  given  as  a  Gnos- 
tic value  of  Christ.  (Moses,  345  ;  I  am  that  I  am,  543.) 
(6.)  If  one  counts  the  days  of  the  solar  year  frorjj  equi- 
nox to  equinox,  or  from  solstice  to  solstice,  he  will  find  that 
there  is  not  an  even  division.  March  22,  to  the  end  of 
March,  inclusive,  is  10  days  ;  this,  or  10  -j-  30  -|-  31  +  30  + 
31  _|-  31  -|-  22  =  185  days,  and  365  —  185  =  180  days,  for 
the  other  half,  showing  a  preponderance  of  5  daj-^s  in  the 
upper  half.  Include  the  solstice  days  in  the  lower  half, 
then  the  upper  half  has  183  days,  and  365  — 183  =  182  ; 
showing  a  diflerence  of  i  day  as  surplus  preserved  by  the 
upper  half.  As  to  the  solstices,  from  the  22d  June  to_the_^ 
end  of  the  moDll3-p..-mcLu'srv?ris°Q°°Ha^^^  9  -|-  31  -|- 

31  +  30  4-  31  -f  30  +  22  =  184  days,  and  365  —  184  =  181 
days,  shov\?ing  a  difference  of  3  days.  Reverse  by  giving 
the  solstice  days  to  the  other  half,  and  184  becomes  182, 
and  365  —  182  =  183  days,  showing  a  difference  of  i  day. 
(Take  the  form  in  which  180  days  becomes  one  of  the 
sides.  This  was  the  number  of  years  of  the  life  of  Abra- 
ham. Add  the  life  of  Isaac  =  175  years,  then  180  +  175 
=  355  ;  where,  to  make  the  36o-3'-ear  period,  requires  just 
5  days.     Add  this  to  175,  and  we  have  for  the  Isaac  side 


/ 


290  Appendix  VII.  §  96. 

180  also,  and  180  X  2  =  360,  or  a  year  period  of  an  exact 
balance.  To  perfect  the  other,  or  365-day  year,  another 
5  days  has  to  be  added ;  which  heretofore  we  have  found 
to  be  added  to  the  lower  half,  or  about  the  time  of  the  17th 
day  of  the  2d  month,  giving  the  preponderance  to  the  lower 
half  of  the  year  of  5  days,  instead  of  to  the  upper,  as 
above.  However,  we  see  that  by  the  addition  of  the  5  days, 
the  balance  is  disturbed.)  It  was,  perhaps,  this  inequality, 
or  preponderance  of  one  side  over  the  other  of  the  year, 
which  went  to  make  up  the  mark  on  Cain,  who  was  a 
nodder,  or  wahbler^  or  "wanderer  in  foreign  lands,"  having 
reference  to  the  unequal  motion  of  the  earth  with  relation 
to  the  ecliptic  in  its  nodding.  There  had  to  be  a  variation 
from  a  fixed  standard  of  division,  as  of  an  even  division, 
to  complete  the  natural  year  in  its  period  of  days.  This 
seems  to  be  implied  in  Cain's  expression,  '•'•My  sin  is 
greater  than  I  can  bear^^''  where  the  equivoque  is  perfect. 
The  two  salient  words  are  sin  and  bear,  related  with  each 
other  by  the  comparative,  i.  e.,  greater.  These  two  words 
are  very  remarkable.  They  are  :  _/(?r  my  sin,  dvoni,  or 
*^1i?,  and  ioxthaji  I  can  bear,min'sho,  or  NIJTJ  — D-  A  bet- 
ter translation  is:  "My  descending  is  greater  than  my 
ascending^''  or  "  my  left  side  is  greater  than  my  right 
side."  The  word  pj7,  dvon,  has  the  meaning  of  sin,  or  of 
copulation,  or  of  ihe  Jem initie  quality — found  in  various 
ways,  as  nothingness,  hollow,  as  given  already ;  and  also 
the  left  side  by  comparison.  Rachel,  in  dying,  brings 
forth  Ben — oni,  or  01^  — p,  whom  she  calls  '•'■  son  of  my 
guilt,  or  sorrow,"  as  it  is  translated ;  but  while  he  is  this 
kind  of  a  son,  as  related  to  her  feminine  quality  of  woman, 
he  was  designated  in  another  way  by  Jacob,  who  changes 
his  name  at  once,  or  in  contrast,  to  Ben — faniin,  or  '-'•  son 
of  my  right  side,"  or  of  the  ^^  light,  clear  region,  the  day 
side"  as  contrasted  with  sin,  woman,  dark,  or  left  side. 
So,  also,  these  words  give  the  idea  of  male  side,  as  con- 
trasted W\\h  female  side.  In  4th  Gen.  7,  as  already  used, 
are  the  words,  "  if  thou  doest  well,  there  is  dignity,  excel- 
lence,  lifting  up,  exaltation,"  as  in    contrast  with   "5m 


§  96.  Appendix  VII.  291 

licth  as  a  cofidairix  at  the  door.''''  The  contrast  word  of 
lifting  tip,  etc.,  is  scath,  nNJT,  from  NC^^,  ndsd.  Now, 
this  word  is  to  be  found  as  applied  to  Reuben  by  his  father, 
Jacob,  where,  by  the  translation,  it  is  the  excellency  of 
dignity,  and  where  the  words  JlNt^  *^^^  yeter  seath,  can 
be  the  prominence  of  my  male  part,  for  immediately  before 
is  the  sentence,  ^'' the  begitining  of  my  strength,''^  where 
for  strength  is,  ''^^'^,  dvoni,  which  is  the  same  with  Rachel's 
*^1J/,  dvoni,  or  femininity;  and  can  be  used  as  the  begin- 
ning of  my  sorrow,  in  the  sense  of  iny  source  of  bcgct- 
tings^  This  description  is  laying  the  foundation  for  the 
conclusion,  which  is,  "unstable  as  water,  thou  shalt  not 
excel."  Why?  "Thou  wentest  up  to  thy  father's  bed; 
then  defiledst  thou  it :  he  went  up  to  my  couch."  Here  is 
an  instance  of  what  Iraneeus  says,  as  quoted  above.  Par- 
aphrased, the  intent  is,  "  Reuben,  thou  art  my  first  born, 
my  eldest ;  who,  by  right  of  primogeniture,  art  the  repre- 
sentation of  myself:  as  such,  thou  art  myself  as  to  the 
place  of  begettings,  and  the  mean  of  begetting,  because 
thou  dost  represent  me.  .  .  .  Yet  wentest  thou  up,"  etc. 
But  to  this  purpose,  here  scath  and  avoni  are  used  as  meni- 
brum  virile  and  yoni.  But  further,  when  Jacob  wrestles 
with  the  angel,  he  does  so  in  the  dark ;  and  as  he  caught 
the  heel  of  his  brother,  so  now  Esau  as  the  angel  (see 
Nork,  Worterbuch)  wrestles  with  Jacob.  The  conclusion 
of  the  wrestling  is  that  Jacob's  thigh  is  dislocated,  or  is 
wasted,  or  shrunken,  as  to  its  sinew.  This  sinew  which 
shrank  is  the  same  word  with  scath,  JIJ^IT,  from  i^CO,  for 
"  KC^:,  with  suffix  \S*:rj,  then  Nn::*,  more  frequently  ilXC^." 
(Fuerst.)  Now,  while  JVdsd,  KC^J,  is  to  raise  up,  to  ex- 
tend upward,  to  rise  high,  ndshd,  T\'^^,  is  to  extend,  stretch 
out,  showing  the  sameness  of  the  words  as  cognate  :  then 
there  comes,  as  related,  Hl^'J,  nashd,  the  large  hip  sinew; 
and,  in  fact,  the  rabbinical  reading  of  this  is,  according  to 
Nork,  ''  spannader  fiir  den  phallus,  7X',!2n  "IDJ^."  (See 
under  Jacob.)  So  also,  it  could  be  taken  as  the  assump- 
tion of  the  feminine  quality  in  this  wrestling.  After  this 
struggle  in  the  dark,  his  name  is  changed  from  its  feminine 


292  Appendix  VII.  §  96. 

character  of  Jacob  to  Israel,  altogether  masculine,  implying 
here  the  change  from  the  dark  to  the  light  part  of  the  year, 
the  boundary  line  between  which  was  the  brook  which  he 
crossed,  or  Pani-El,  or  the  division  line  at  the  solstice,  pre- 
cisely as  in  the  description  of  Cain,  as  going  up  from  Tobi 
and  descending  from  Pani,  the  same  solstice  line  is  desig- 
nated. Under  "Jacob,"  Nork  says  :  The  cardinal  or  hinge 
point  is  "therefore  called  Pani-El  (7X"*J£3),  i.  e.,  change 
or  turning  oi  the  {time)  god,  that  place  where  Jacob 
wrestled  with  the  demon,  in  whom  the  rabbins  recocrnize 
Esau,  from  whom  the  name  of  the  boundary  river  Jabbok 
(pD*  V.  pD5»{,  to  wrestle),  and  overcome  him."  Pani-El  and  .^ 
Jabbok  are  used  interchangeably.  ^ 

His  going  up  was  Scath,  or  male,  and  his  descending  r 
was  on  the  other  side  toward  the  characteristic  of  that  side  C 
— \\z.,  /einale.  The  male  was  his  right  side,  the  female 
was  his  Ic/t  side.  Now  from  summer  solstice  to  winter 
solstice  is  9  +  31  +  31+30+31+30+22=184  days, 
and  365  — 184  =  181  ;  so  that  the  female  side  was  greater 
than  the  male  side  by  3  days.  Or,  considering  the  circle 
of  the  year  as  the  form  of  a  man-w^oman,  his  left  side  at 
the  hip  would  be  greater  than  his  right  side ;  or,  his  sin 
side  was  greater  than  his  male  side.  And  this  goes  to 
show  that  the  glyphs  of  Cain  and  Abel,  and  of  Jacob  and 
Esau,  are  to  this  extent  alike,  as  having  reference  to  the 
same  phenomenon.  Now  as  to  the  mark  set  on  Cain. 
The  words  are  fllJ^  fpS  Hl.T  DC^^,  V'yasem  Yehovah 
I'kayin,  oth,  where  the  predicate  yasem,  Dt^*%  is  the  apoca- 
pated  future  hifil,  from  shivm,  Dli^.  Of  this  word  under 
(11.),  Fuerst  says:  "  Properly,  to  be  veiled,  hence  to  be 
obscured,  darkened;  metaphor,  to  be  impotent,  weak;  fig., 
to  be  on  the  left — the  left  side  being^re^rarded  ^^jJie  weak 
-  one^  the  left  district  as  the  obscured,  concealed  one.  See 
pflV,  Tsafhon;  SkOC^'  Samaeir  Tsaphon  "is  the  dark, 
wintry  hemisphere,  the  dark  region,  where  the  sun  and  the 
stars  are  extinguished,  and  the  light  of  heaven  is  swallowed 
up."  Samacl  "is  the  veiled,  dark  region  of  the  north; 
what  is  turned  to  the  north,  the  left  side,  the  left  hand.'' 


§  9^- 


Appendix  VII. 


293 


It  was  reported,  rabbinically,  that  Kin  (Cain)  the  Evil  was 
the  son  of  Eve  by  Samael  the  devil,  who  occupied  the 
place  of  Adam. 

So  the  reading  of  the  line  is  :  "Aild__thfi_LDriLcaused 
impotence  to  Cain,  or  weakness,  or  loss,  on  the  left  side,  as 


a  mark  or  token,"  etc. ;    and  this  corresponded  with  the 
lameness  of 


and  also  with  the  lameness  of  Vulcain. 
This  impotencelias  nothing  to  do  with  the  left  side  being 
the  largest,  but  with  its  female  quality  ;  for  it  is  ascribed  by 
the  rabbins  to  that  of  the  virile  power,  which  is  extin- 
guished in  the  dark  or  female  part  of  the  year,  which 
commences  with  the  vintage,  the  sun  in  Scorpio,  just  where, 
by  the  Persian  symbolization,  the  Bull  suffers  castration  by 
the  Scorpion,  or  just  where  the  ^  of  Jehovah  conceals  itself 
in  HovaTT. 
'■'"^"T(7t)==-As"  one  after  another  of  the  allegorical  uses  comes 
up,  and-  is  explained,  the  aggregation  all  tending  to  one 
elucidation,  serves  to  clear  away  the  ambiguity  and  equiv- 
ocation from  the  remainder.  It  is  seen  how  fitly  the 
Egyptian  mode  of  hieroglyphic  expression  fits  to  the  He- 
brew use.  As  there  was  a  common  underlying  use  in 
numbers  and  geometrical  forms,  as  in  the  Bible  there  is 
constant  reference  to  a  mysterious  connection  between  the 
Hebrews  and  the  Egyptians,  so  there  seems  to  have  been 
an  interchangeable  use  of  a  common  mode  of  expression. 
This  accords  with  the  statement  of  Seyffarth  (Chro.,  p.  34)  : 

"  Now,  we  know  that  with  Abram,  1 150  years  after  the  flood, 
484  yeai"s  after  Phaleg,  during  whose  life  the  Egyptians  and  all 
the  other  ancient  nations  emigrated  from  Babylonia — i.  e.,  2781 
B.  c.-— the  Hebrews  left  their  original  jolace  of  abode.  These 
Abramidae  spoke  Hebrew,  and  consequentl}'  this  same  language 
inust  have  been  indigenous  in  Chaldea.  But  as  Menes  also  came 
from  Chaldea  only  484  years  before  Abraham,  the  ancient 
Egyptian  language  7nust  be  itztimately  related  to  the  HebrexvP 

And  this  agrees  with  what  one  so  frequently  finds  as  to 
the,  by  statement,  passing  over  of  old  Phenician  radicals  into 
the  formation  of  hieratic  words,  to  the  Egyptians,  Babylon- 
ians, even  Hindus,  Greeks,  Latins,  Germans,  and  espe- 
cially British,  showing  a  common  reservoir  of  knowledge 


294  Appendix  VII.  §  96. 

for  all  these  ancient  people.  Already  we  have  seen  this 
to  be  the  case  as  to  Arcts,  Mars,  Tobi,  and  Pani,  in 
especially  hieroglyphic  connections.  The  equivocation  in 
the  narrative  scene  of  Cain  and  his  brother  Abel,  as  to  the 
slaying,  as  to  "  cursed  art  thou,"  as  to  "  my  sin  is  greater 
than  I  can  bear,"  is  perfect.  But  these  are  preceded  by 
one  just  as  great  in  the  words  of  warning  to  Eve.  The 
Garden  scene  was  the  picture  of  that  sinful  transgression 
culminating  in  the  universal  fall  of  man  (or  better,  of 
woman),  bringing  upon  an  innocent  progeny  unnumbered 
woes.  In  the  very  first  exertion  of  his  divine  power,  God, 
we  are  led  to  infer  from  the  simple  narrative,  set  a  trap  for 
his  most  simple-minded  and  ignorant  son  and  daughter. 
There  seems  to  be,  on  the  face  of  this  "as  in  Adam  all 
fell,"  a  sort  oi  non  scquittir,  as  relates  to  the  honorable  and 
merciful  character  of  the  inventor.  But,  manifestly,  and 
to  speak  seriously,  as  relates  to  humanity,  the  Garden  was 
the  scene  of  the  creation  of  and  first  recognition  by  the 
sexes  of  their  difference  of  organism  ;  also  of  their  sexual 
introduction  the  one  to  the  other.  Now,  the  little  deeper 
reading  of  the  narrative  turns  the  mask  and  shows  the  nat- 
ural and  true  intent,  thus  spoiling  the  equivocation.  While 
Adam  was  in  the  hermaphrodite  condition — i.  e.,  before  the 
woman  was  taken  from  him — he  or  she  is  told  as  to  the  for- 
bidden fruit,  "  for  in  the  day  thou  eatest  of  it,  dying  thou 
shalt  die"  (Gen.  ii.  17.)  illQ,  muth,  dying,  mOD,  Td- 
muth,  thou  shalt  die.  That  this  was  said  to  her  is  clearly 
implied  in  verse  3  of  the  third  chapter,  where  the  words  are 
the  same.  The  following,  as  to  the  Egyptian,  will  lend 
further  and  singular  reflections  on  this  subject : 

'•'■Mtith,  or  Mouth,  was  the  Egyptian  cognomen  of  Venus  (Eve, 
mother  of  all  living),  or  tJie  moon.  Plutarch  (Is.  374)  hands  it 
down  that  '  Isis  was  sometimes  called  Aluth,  which  word  means 
mother.  Either  Man,  or  Alaut^  means  nurse,  mother.  Perhaps 
Muth  is  to  be  derived  from  j\Ian-tho^  materterra  (Eve-Adam), 
which  being  the  fact,  Muth  differs  in  nothing  from  Isis,  queen  of 
the  earth  (Issa,  Hl^J^'  tuotnan).'  (Is.,  p.  372.)  Isis,  he  says,  is 
that  part  of  nature  wliich,  as  feminine,  contains  in  herself,  as 
(nutrix)   nurse,   all  things  to  be  born.     '  Certainly  the  moon,* 


§  96.  Appendix  VII.  295 

speaking  astronomically,  '  chiefly  exercises  this  function  in 
Taurus,  Venus  being  the  house  (in  opposition  to  Mars, _^e«er- 
a^or,  in  Scorpio),  because  the  sign  is  luna,  ]),hypsoma.  Since 
truly  it  may  be  taken  from  this  passage  of  Plutarch,  that  Isis 
Metheur  diflers  from  Isis  JSIuth^  and  that  in  the  vocable  Aliith^ 
the  notion  of  bringing  forth  may  be  concealed,  and  since  fruc- 
tification must  take  place,  Sol  being  joined  with  Luna  in  Libra, 
it  is  not  improbable  that  Muth  first  indeed  signifies  Venus  in 
Libra  ;  hence  Luna  in  Libra."  (Beitrage  zur  Kenntniss,  pars 
II,  §  9,  under  Aluth.) 

Now  there  is  not  a  word  of  this  description  which  is  not 
fitted  to  the  scope  of  the  Garden  of  Eden  glyph.  It  is 
part  and  parcel  of  the  same  learning  that  gives  the  Egyptian 
ARTS,  as  the  Phenician  and  Hebrew  ARTS,  in  the  first 
chapter  of  Genesis.  Now  consider  the  correlating  terms, 
Sin  with  Intercourse,  and  the  symbol  of  death  being  but 
that  of  birth,  as  they  have  relation  to  the  place  Scorpio, 
the  opposite  to,  yet  connected  in  the  center,  with  Taurus- 
Venus,  and  the  conclusion  is  irresistible,  that  in  the  words 
''dying  thou  shalt  die''  (that  is,  in  Scorpio),  we  have  by 
correlative  reading  and  meaning  "  conceiving  thou  shalt 
become  a  mother''  And  this  agrees  with  the  fact  related  ; 
for  she  did  eat  the  fruit,  she  did  not  die,  and  she  did  be- 
come a  another.  This  shows  the  double  play  upon  the  word 
Muth,  nits,  by  help  of  which  the  real  intent  is  produced  in 
the  occult  way,  as  intended.  Sin,  death,  and  woman  are 
one  in  the  glyph,  and  are  correlatively  connected  with  in- 
tercourse and  birth.  This  derivation  once  stated,  finds 
full  confirmation  on  its  own  Phenician,  or  Hebrew  soil. 
The  word  Bohu,  IHD,  void,  has  been  seen  to  be  taken  for 
Eve-Venus-Naamah.     Fuerst,  under  Bohu,  IHD,  says  : 

"  In  this.primitive  signification  was  IH^  taken  in  the  Biblical 
cosmogony,  and  used  in  establishing  the  dogma  (j^NQ  V\  fcs- 
(us),  niaven,  Jes-us  from  nothing^,  respecting  creation. 
Hence,  Aquila  translates  ov6h,  vulg.  vacua  "  (hence  vacca,  co-w), 
"  Onkelos  and  Samarit,  ^^pH-  The  Phenician  cosmogony  has 
connected  Bohu,  Ipf;^,  Baof,  into  a  personified  expression  denot- 
ing the  primitive  substance,  and  as  a  deity,  the  mother  of  races 
of  the  gods.  TheAramean  name  n'lilD.  il'inD-  ^{n"*I^D' Baa;.!f, 
Bi.i9-of,  Buto,  for  the    mother  of  the  gods,  which  passed  over  to 


296  Appendix  VII.  §  96. 

the  Gnostics,  Babylonians,  and  Egyptians,  is  identical  then  with 
Mot  (niD»  our  Muth),  properly,  Biii^  (ri""in^),  originated  in 
Phenician  from  an  interchange  of  b  with  mP 

This  .view  assists  also  to  another  facility  for  interpreta- 
tion. Each  sign  to  be  mentioned  was  a  double  sign,  or 
male-female — viz.,  it  was  Taurus-Eve,  and  Scorpio  was 
Mars-Lupa,  or  Mars  with  the  female  wolf.  So,  as  these 
signs  were  opposites  of  each  other,  yet  met  in  the  center, 
they  were  connected  ;  and  so  in  fact  it  was,  and  in  a  double 
sense,  the  conception  of  the  year  was  in  Taurus,  as  the 
conception  of  Eve  by  Mars,  her  opposite,  in  Scorpio.  The 
birth  would  be  at  the  winter  solstice,  or  Christmas.  On 
the  contrary,  by  conception  in  Scorpio — viz.,  of  Lupa  by 
Taurus — birth  would  be  in  Leo.  Scorpio  was  Chrestos  in 
humiliation,  while  Leo  was  Christos  in  trium-ph.  While 
Taurus-Eve  fulfilled  astronomical  functions,  Mars-Lupa 
fulfilled  spiritual  ones  by  type. 

The  workings  out  of  this  glyph  of  4th  Genesis  help  to 
the  comprehension  of  the  division  of  one  character  into  the 
forms  of  two  persons  ;  as  Adam  and  Eve,  Cain  and  Abel, 
Abram  and  Isaac,  Jacob  and  Esau,  and  so  on.  It  helps, 
also,  to  take  the  horrid  blemish  off  from  the  name  of  Cain, 
as  a  put-up  job  to  destroy  his  character ;  for,  even  without 
these  showings,  by  the  very  text,  he  was  Jehovah.  So  the 
theological  schools  had  better  be  alive  to  making  the  amend 
honorable,  if  such  a  thing  is  possible,  to  the  goodnameand 
fame  of  the  God  they  worship. 

(8.)  Now,  as  linking  together  several  great  salient 
points  in  the  Biblical  structure:  (i.)  As  to  the  Old  and 
New  Testaments  ;  with,  also,  (2.)  as  to  the  Roman  empire  ; 
(3.)  as  to  confirming  the  meanings  and  uses  of  sym- 
bols ;  and  (4.)  as  to  confirming  the  entire  explanation  and 
reading  of  the  glyphs  as  (5.)  recognizing  and  laying  down 
the  base  of  the  great  pyramid  as  ihe  foundation  square  of 
the  Bible  construction,  (6.)  as  well  as  the  New  Roman 
adoption  under  Constantine — the  following  is  given  : 

Cain  has  been  shown  to  be  the  144 — 441  form  of  the 
Garden,  based  upon  a  square  of  144  X  144  in  the  center. 


§  96. 


Appendix  VII. 


297 


He  has  been  shown  to  be  the  360  circle  of  the  zodiac,  the 
perfect  and  exact  standard,  by  a  squared  division  ;  hence 
his  name  of  Melchizadik.  He  has  been  shown  to  be  the 
distributer  or  adjuster  of  the  365-day  year  on  this  square 
of  360  or  36.  The  Hebrew  year  has  been  shown  to  be  the 
base,  in  Abram,  180  +  Isaac,  175  =  355.  This  +  5  =  360, 
or  Cain,  and  3554-10  =  365,  by  which  the  solstice  and 
equinox  points  of  the  360  or  zodiac  (or  life)  circle  are  made 
to  fall  back,  as  to  the  months  of  the  365-day  year,  so  that 
the  equinox  points  shall  fall,  as  for  months,  on  ihejfirst  day 
of  October^  or  Scorpio,  and  its  opposite  ;  while  the  solstices 
are  to  be  marked  by  Leo  and  its  opposite.  This  was  a 
Hebrew  use  and  recognition  under  the  squared  form  ;  they 
taking  out  the  3d  quadrant,  cube,  of  which  Leo  and  Libra, 
bordering  on  Cancer  and  Dan-Scorpio,  were  the  corner 
controllers.  But  this  corner  cube,  worked  in  on  to  the 
square  of  the  entire  year,  was  made  to  preserve  this  same 
order,  by  Leo  and  Dan-Seorpio  being  made  to  hold,  re- 
spectively, the  two  controlling  corners  of  the  great  square. 
Now,  this  was  all  founded  on  the  Cain-Adam  square  ;  or, 
as  shown,  the  square  of  the  base  of  the  great  pyramid. 
Take  this  square,  as  the  Cain-Adam  square  of  144 — 441, 
with  the  central  or  Ada^n  square  of  12X12  =  144  (either 
as  a  line  or  as  area)  ;  and,  holding  the  numerical  value  as 
inches,  take  the' "Same  square,  as  reduced  to  feet: 


1 

1 

S 

3 

4' 

2 

1 

A 

■ 

By  the  very  force  of  construction,  the  larger  square  will  be 
laid  off  into  blocks  of  6  X  6  feet,  and  its  circumference  will 
exhibit  a  face  divided  into  12  of  these  squares,  and  12X6 


298  Appendix  VII.  §  96. 

=  72  feet,  or  for  a  line  circumference  of  24  X  4  =  96  feet ; 
while  the  interior  or  Adam  square  is  shown  to  be  divided 
into  4  blocks  of  6  X  6  feet  each.  It  has  been  repeatedly 
stated  that  the  object  of  the  great  pyramid  construction  was 
to  measure  the  heavens  and  the  earth;  therefore,  its  meas- 
uring containment  would  indicate  all  the  substance  of 
measure  of  the  heavens  and  the  earth,  or  agreeably  to  an- 
cient recognition,  Earth,  Air,  Water,  and  Fire.  (The 
base  side  of  the  pyramid  was  diameter  to  a  circumference 
vn  feet  of  2400.  The  characteristic  of  this  is  24  feet,  or 
6X4  =  24,  or  this  very  Cain-Adam  square.)  Now,  by  the 
restoration  of  the  encampment  of  the  Israelites,  as  initiated 
by  Moses,  by  the  great  scholar,  Father  Athanasius  Kircher, 
the  Jesuit  priest,  the  above  is  precisely,  by  Biblical  record 
and  traditionary  sources,  the  method  of  laying  off  this  en- 
campment. The  four  interior  squares  were  devoted  to 
(i.)  Moses  and  Aaron;  (2.)  Kohath ;  (3.)  Gershon  ;  and 
(4.)  Merari — the  last  three  being  the  heads  of  the  Levites. 
The  attributes  of  these  squares  were  the  primal  attributes 
of  Adam-Mars,  and  were  concreted  of  the  elements. 
Earth,  Air,  Fire,  Water;  or  D^  ^  lam  =  Water,  "llj  = 
Nour  =  Fire,  (11")  =  Rouach  =  Air,  and  T\^'y  =  Idbeshah 
==  Earth.  The  initial  letters  of  these  words  are  INRI. 
This  square  of  INRI  is  the  Adam  square,  which  was  ex- 
tended from,  as  a  foundation,  into  four  others  of  144  X  2 
=  288,  to  the  side  of  the  large  square,  and  288  X  4  = 
1 15-2,  =:  the  whole  circumference.  But  this  square  is  the 
display  of  also  circular  elements,  and  11 5-2  can  denote 
this.  Put  INRI  into  a  circle,  or  read  it  as  the  letters  stand 
in  the  square,  as  to  its  values  of  1521,  and  we  have 


which  reads  115-2  of  this  fact.     But,  as  seen,  Cain  denotes 
this  as,  or  in,  the  115  of  his  name  ;  which  115  was  the  very 


§  96.  Appendix  VII.  299 

complement  to  make  up  the  360-day  year,  to  agree  with 
the  balances  of  the  standard  circle,  which  were  Cain.  The 
corner  squares  of  the  larger  square  are,  A=  Leo,  and  B  = 
Dan-Scorpio ;  and  it  is  seen  that  Cain  pierces  Abel  at  the 
intersection  of  the  equinoctial  with  the  solstice  cross  lines, 
referred  to  from  Dan-Scorpio,  on  the  celestial  circle.  But 
Dan-Scorpio  borders  on  Libra,  the  scales,  whose  sign  is 
=0=  (which  sign  is  that  of  the  ancient  -pillow,  on  which 
the  back  of  the   head  to  the  ears  rested,  the  pillow  of 

Jacob),  and  is  represented  for  one  symbol  as   ^ — — — r 

as  has  been  shown.     But  also  the  badge  of  Dan-Scorpio 


J 


is  death-life,  in  the  symbol      f~   as  cross-hones  and  skulls 

or  back  of  the  head,  or  life-death ;  and  this  was  the  mono- 
gram of  Chr'estos,  and  the  Labarmn,  or  standard  of  Constan- 
tine,  the  Roman  emperor.  Abel  has  been  shown  to  be 
Jesus,  and  Cain-Vulcain,  or  Mars,  pierced  him.  Constan- 
tine  was  the  Roman  emperor,  whose  warlike  god  was  Mars, 
and  a  Roman  soldier  pierced  Jesus  on  the  cross  ;  so  that 
the  three  unite  under  this  characteristic.  But  the  piercing 
of  Abel  was  the  consummation  of  his  marriage  with  Cain, 
and  this  was  proper  under  the  form  of  Mars-Generator ; 
hence  the  double  glyph,  one  of  Mars-Generator  and  Mars- 
Destroyer  in  one ;  significant,  again,  of  the  primal  idea  of 
the  living  cosmos,  or  of  birth  and  death,  as  necessary  to 
the  continuation  of  the  stream  of  life.  Now,  the  cross  is 
the  emblem  of  the  origin  of  measures,  in  the  Jehovah 
form  of  a  straight-line  one  of  a  denomination  of  20612,  the 
■perfect  circumference ;  hence  Cain  was  this  as  Jehovah, 
for  the  text  says  that  he  was  Jehovah.  But  the  attachment 
of  a  man  to  this  cross  was  that  of  113  :  355  to  6561  :  5153 
X  4—  20612,  as  shown.  Now,  over  the  head  of  Jesus  cru- 
cified was  placed  the  inscription,  of  which  the  initial  letters 
of  the  words  have  always  been  retained  as  symbolic,  and 
handed  down  and  used  as  a  monogram  of  Jesus  Chrestos — 


300  Appendix  VII.  §  96. 

viz.,  INRI,  or  Jesus  Nazarenus  Rex  ytidcsorum ;  but  they 
are  located  on  the  cross  or  the  cubed  yt?rw  of  the  circular 
origin  of  measures,  which  measure  the  substance  o{  £arth, 
Air,  Fire,  and  Water,  or  INRI  =  1152,  as  shown.  Here 
is  the  7nan  on  the  cross,  or  113  :  355  combined  with 
6561  :  5153  X  4  =  20612.  These  are  the  fyramid-base 
numbers,  as  coming  from  113  :  355  as  the  Hebrew  source  ; 
whence  the  Adam  square,  which  is  the  pyramid  base,  and 
the  center  one  to  the  larger  square  of  the  enca7npment. 
Bend  INRI  into  a  circle,  and  we  have  1 152,  or  the  circum- 
ference of  the  latter.  But  Jesus  dying  (or  Abel  married) 
made  use  of  the  very  words  needed  to  set  forth  all.  He 
says  Eli  Eli  Lamah  Sabachth-ani 

For,  read  them  by  their  power  values,  in  circular  form,  as 
produced   from  the  Adam  form,  as  shown,  and  we  have 

*7K  =  113,  "h^  =  113,  or  113 — 311:  (ID?  =  345,  or 
Moses  in  the  Cain-Adam  pyramid  circle:  nflDiT  =  710, 
equals  Dove,  or  Jonah,  and  710  h-  2  =  355,  or  355—553  ; 
and  finally,  as  determinative  of  all,  J%  or  7ii,  where  ^  = 
TVz/w,  fish  =  565,  and  *  =  I  or  10;  together  565i=mnS 
or  the  Christ  value. 

And  thus  closes  the  relation  between  the  Parker  and  Me- 
tius  forms  of  numbers  in  construction  of  the  great  pyramid, 
with  their  Biblical  use  ;  and  it  is  seen  that  the  pyramid 
sto7ie  book  is  the  equivalent  of  the  Old  and  New  Testaments. 


Attention  is  called  to  part  of  the  46th  verse  of  the  27th 
chapter  of  Matthew,  as  follows  :  "  Eli,  Eli,  Lama  Sabach- 
thani? — that  is  to  say.  My  God,  my  God,  wh}'^  hast  thou 
forsaken  me?"  Of  course,  our  versions  are  taken  from  the 
original  Greek  manuscripts  (the  reason  why  we  have  no 
original  Hebrew  manuscripts  concerning  these  occurrences 
being  because  the  enigmas  in  Hebrew  would  betray  them- 
selves on  comparison  with  the  sources  of  their  derivation, 
the  Old  Testament).  The  Greek  manuscripts,  without  ex- 
ception, give  these  words  as — 


§  96.  Appendix  VII.  301 

They  are  Hebrew  words,  rendered  into  the  Greek,  and  in 
Hebrew  are  as  follows  : 

rrnnn::'  no?  h^  ^\v 

The  Scripture  of  these  words  says,  "  that  is  to  say,  My 
God,  my  God,  why  hast  thou  forsaken  me?"  as  their 
proper  translation.  Here  tlien  are  the  words,  beyond  all 
dispute;  and  beyond  all  question,  such  is  the  interpreta- 
tion given  of  them  by  Scripture.  Now  the  words  will  not 
bear  this  interpretation,  and  it  is  a  false  rendering.  The 
true  meaning  \sjust  the  o^pposite  of  the  one  given,  and  is — 

My  God,  my  God,  how  thou  dost  glorify  mel 
But  even  more,  for  while  lama  is  why,  or  how,  as  a  verbal 
it  connects  the  idea  of  to  dazzle,  or  adverbially,  it  could  run 
"  how  dazzlingly,''  and  so  on.  To  the  unwary  reader  this 
interpretation  is  enforced  and  made  to  answer,  as  it  were, 
to  the  fulfillment  of  a  prophetic  utterance,  by  a  marginal 
reference  to  \}i\Q.  first  verse  of  the  twenty-second  Psalm, 
which  reads  : 

"  My  God,  my  God,  why  hast  thou  forsaken  me?" 
The  Hebrew  of  this  verse  for  these  words  is — 

as  to  which  the  reference  is  correct,  and  the  interpretation 
sound  and  good,  but  with  an  utterly  different  word.  The 
words  are — 

Eli,  Eli,  lamah  azabvtha-ni9 
ISJo  wit  of  man,  however  scholarly,  can  save  this  passage 
from  falseness  of  rendering  on  its  face  ;  and  as  so,  it  be- 
comes a  most  terrible  blow  upon  the  proper  first-tace 
sacredness  of  the  recital.  There  is  but  one,  and  there  is 
one  escape,  and  that  is  by  having  resort  to  the  mystical  in- 
tent. The  Hebrew  phrase  was  -purfoscd  as  it  reads,  and 
its  antagonistic  and  false  rendering  was  furfosed  as  it 
reads.  It  was  on  the  same  principle  already  mentioned,  of 
the  crossed  bones  and  skull,  as  an  emblem  of  death,  being 
placed  over  the  door  of  life  and  signifying  birth,  or  of  the 
intercontainment  of  two  opposite  principles  in  one,  just  as, 
mystically,  the  Savior  was  held  to  be  man-woman.  This 
was  the  idea  intended,  and  interpreted  thus,  the  passage 


302  Appendix  VII.  §  96. 

suffers  no  violence  of  distortion.  Above,  the  numerical 
values  of  the  words  have  been  given,  as  connecting  them- 
selves with  the  INRI,  or  288X4  =  1152,  of  the  inner 
square  and  outer  square  of  the  encampment,  which  at  the 
same  time  is  the  base  of  the  pyramid,  by  equivalence. 
But  by  these  numbers,  Eli  is  113  (by  placing  the  word  in 
a  circle) ;  Lamah  being  345,  is  by  change  of  letters  to  suit 
the  same  values  HC^D  (in  a  circle),  or  Moses,  while  Sa- 
bachth  is  John,  or  the  dove,  or  Holy  Spirit,  because  (in  a 
circle)  it  is  710  (or  355  X  2).  The  termination  «/,  as  mini^ 
or  565''  becomes  Jehovah.  Connecting  this  phrase  with 
INRI,  and  it  throws  light  upon  the  transfiguration  scene  on 
the  mount.  There  were  present  there  Peter  and  James 
and  John  with  Jesus:  or  D%  lami,  James,  water;  XW^ ^ 
Peter,  earth;  T\T\,  John,  spirit,  air,  and  "11^,  Jesus,  fire, 
life — together  INRL  But  behold  Eli  and  Moses  met  them 
there,  or  *^j^  and  n,tD7'  °'"  -EH  and  lamah,  or  113  and  345. 
And  this  shows  that  the  scene  of  transfiguration  was  con- 
nected with  the  one  above  set  forth. 


As  closing  these  appendices,  it  is  thought  appropriate 
and  instructive  to  insert  some  comments  upon  the  ^^ Study 
of  the  Bible,"  made  by  a  clergyman  of  New  York  city, 
and  published  in  the  Tribune.  The  difficulties  surround- 
ing the  text  of  the  Bible,  as  received  and  interpreted,  for  a 
satisfactory  comprehension  of  the  contents  of  The  Book, 
are  ably  and  clearly  set  forth.  Their  setting  forth  seems 
to  point  to  the  existence  of  a  key  of  interpretation  not  as 
yet  known  or  made  use  of.  That  part  of  these  comments 
which  is  thought  pertinent  to  the  present  inquiry,  is  as  fol- 
lows : 

"  The  Church  is  to  conserve  the  Scriptures,  because  they  con- 
serve the  Church.  The  Jewish  Church  made  the  mistake  of  con- 
serving the  mere  letter,  and  hence  became  corrupt.  The  Scrip- 
tures are  not  the  letter,  but  the  spirit  beneath  the  letter,  reached 
by  the  letter.  The  Church,  then,  rightly  conserves  the  Scriptures 
when,  by  diligent  investigation  through  and  beneath  the  letter,  it 
binds  the  varied  truth  of  God  fast  to  its  life  by  a  thousand  cords 
of  knowledge  and  affection.     With  this  view,  then,  of  the  study 


§  96.  Appendix  VII.  303 

of  the  letter  of  Scripture  as  the  necessary  avenue  to  reach  its  di- 
vine ti'uths,  and  as  thus  following  the  injunction  of  the  Savior  in 
the  text,  we  may  notice  three  classes  of  difficulties  which  invite 
this  study,  and  to  the  solution  of  which  the  careful  and  concen- 
trated search  is  essential. 

"  The  first  difficulty  is  the  apparent  want  of  harmony  in  the 
different  portions  of  the  sacred  volume.  This  has  been  the  favor- 
ite battle-ground  of  infidelity.  Here  it  uses  with  effect  its  argu- 
jncntum  ad  speciem^  and  makes  its  crafty  conquests.  The  Eloh- 
istic  and  Jehovistic  chapters  of  Genesis  are  irreconcilable  ;  the 
Pentateuch  bears  marks  of  a  post-Mosaic  origin  in  its  allusions 
to  the  character  and  the  death  of  the  lawgiver ;  the  chronology 
of  the  historical  books  is  hopelessly  confused  and  false ;  the  two 
genealogies  of  Jesus  are  in  direct  conflict ;  all  the  accounts  of  the 
inscription  on  the  ci'oss  are  discrepant ;  indeed,  the  four  Gospels 
present  a  hundred  points  of  difference  and  antagonism.  James 
and  Paul  teach,  as  respects  one  another,  contradictory  doctrines, 
and  the  New  Testament  presents  a  system  of  salvation  and  eternal 
life  wholly  inconsistent  with  that  of  the  Old  Testament.  These 
are  the  chief  charges  that  are  made  where  prima  facie  evidence 
is  on  the  enemy's  side,  and,  as  with  the  majority  of  our  race, 
priina  facie  evidence  is  all  that  men  care  to  have  against  any- 
thing they  wish  to  avoid,  these  charges  gain  a  common  currency, 
and  repeat  themselves  in  every  age.  To  meet  these  charges  and 
their  pernicious  effects,  a  knowledge  of  the  media  through  which 
the  Divine  Spirit  communicated  the  truth  is  necessary.  The 
mind  must  take  a  range  through  1,500  years,  from  Moses  to  John, 
and  examine  the  variations  of  language  and  customs,  the  history 
and  national  economy  of  the  Jewish  people,  as  well  as  those  of 
the  great  kingdoms  of  the  Nile,  the  Tigris,  and  the  Euphrates. 
We  must  recognize  the  full  idiosyncrasy  of  each  sacred  writer 
under  the  divine  afflatus.  It  must  explore  the  analogies  in  expe- 
rience, where  different  standpoints  reveal  apparent  discrepancies. 
It  must  learn  to  weigh  wordb  as  they  are  given  us  in  the  Semitic 
and  Hellenic  tongues,  and  detach  them  from  the  prejudice  of  a 
translation.  It  must  find  the  special  object  that  was  before  a 
writer's  mind,  and  these  special  circumstances  in  which  his  utter- 
ances first  took  place.  It  must  review  the  laws  of  authorship 
and  editorship,  and  determine  their  influence  upon  the  sacred 
books.  It  must  become  familiar  with  the  great  landmarks  of 
chronology,  and  be  able  to  establish  the  synchronisms  of  the 


304  Appendix  VII.  §  96. 

Scripture  narrative.  Only  in  this  way  can  scoffing  infidelity  be 
answered,  and  the  pious  mind  be  edified  by  a  discovery  of  the 
perfect  harmonies  of  the  Divine  Word. 

"  A  second  difficulty  is  akin  to  the  first,  and  can  be  easily  com- 
pared with  it.  It  is  the  obscurity  of  the  text.  It  does  not  appear 
to  contradict  itself,  but  its  very  meaning  is  a  puzzle.  The  ordi- 
nary reader  sees  only  a  chaos,  and  either  looks  over  the  passage 
till  he  finds  some  plain  words  to  satisfy  him,  or  he  performs  the 
dangerous  task  of  guessing  where  he  has  no  data,  and  so  makes 
the  Scripture  to  speak  falsely.  To  overcome  this  difficulty  we 
need  all  the  appliances  which  are  requisite  in  reading  the  alleged 
discrepancies  of  the  Word,  and  these  are  to  be  used  in  an  in- 
tenser  degree.  History  and  geography  must  be  ransacked  and 
arranged  in  the  mind  ;  the  oriental  habits  and  styles  of  thought 
must  be  familiarized  ;  bigotry  and  narrowness  must  be  aban- 
doned for  a  broad  view  of  the  race  and  a  generous  sympathy  for 
human  development  everywhere.  Especially  are  the  two  lan- 
guages of  Scripture  to  be  carefully  studied — the  sterility  of  He- 
brew, whose  obscurity  lies  in  its  poverty,  and  the  flexible  and 
beautiful  Greek,  whose  obscurity  lies  in  its  richness.  The  En- 
glish translation  is  one  of  the  best  ever  made,  perhaps  the  very 
best  after  the  Hollandish,  and  this  English  translation  is  so  en- 
deared to  us  by  tenderest  associations  that  it  would  not  be  wise 
to  set  it  aside  for  another.  If  any  change  be  made,  our  old  ver- 
sion must  remain  the  basis,  and  only  such  alterations  efiected  as 
truth  and  righteousness  demand.  Our  holy  religion  does  not 
require  us  to  be  blind  moles,  but  to  use  our  eyesight  and  discrim- 
inate everywhere  between  the  true  and  the  false.  The  religion 
of  Jesus  courts  the  fullness  of  light,  and  loathes  the  conservatism 
of  conventionality,  prejudice,  and  ignorance.  With  all  the  excel- 
lence of  our  English  version,  it  bears  marks  of  the  human  im- 
perfection of  the  translators,  as  where  they  hide  away  the  word 
'  bishops,'  in  Paul's  address  to  the  elders  of  Miletus,  and  call  it 
'  overseers,'  and  where  they  call  the  Passover  the  heathenish 
name  of  '  Easter.'  Besides  such  willful  errors,  they  erred  often 
through  ignorance  of  the  language  they  translated.  The  Hebrew 
and  the  Greek  are  far  better  understood  to-day  than  in  1611. 

"  But  I  turn  from  the  obscurity  of  tlTe  text  to  a  third  difficulty 
which  demands  search,  to  wit,  the  apparent  collisions  between 
Scripture  and  science.  The  God  of  the  Scriptures  is  the  God  of 
nature,  and  the  explanation  of  nature  will  only  magnify  the 
Scriptures.     We  know  that,  but  we   must  show  it  to  the  world. 


§  96.  Appendix  VII.  305 

The  scientific  investigations  of  this  age  arc  manifold  and  ener- 
getic, and  it  is  for  the  Christian  to  rejoice  in  all  the  discoveries 
which  throw  litrht  on  God's  vs^onderful  works  in  the  material  uni- 
verse.  It  is  for  him  to  follow  the  physical  philosopher,  and  to 
weigh  his  stated  conclusions,  to  judge  whether  they  are  warranted 
by  his  premises  (and  this  does  not  require  a  scientific  knowledge, 
common  sense  will  do  it),  and  then  bring  the  truth  from  God's 
Word,  that  these  truths  from  the  natural  world  may  help  explain 
the  sacred  texts,  just  as  our  historical  or  linguistic  facts  have  been 
used  before.  In  this  way  the  supposed  antagonism  between  ge- 
ology and  Genesis  in  the  questions  of  cosmogony,  the  origin  of 
the  race,  and  the  deluge,  will  be  dissipated,  and  the  light  of  the 
Word  shine  the  more  brightly.  The  lowest  doubts  of  thoughtful 
men  will  be  respected  and  overcome,  and  the  cause  of  truth 
promoted.  It  will  not  do  to  ignore  these  questions.  If  they  at- 
tack God's  Word,  we  must  use  them  as  means  of  searching  God's 
Word.  To  yield  to  the  bold  assertions  of  science  versus  Scrip- 
ture is  weakness  ;  while  to  shut  them  out  from  examination  and 
dogmatically  denounce  them,  is  not  only  weakness  but  meanness. 
The  only  honest  and  manly  way  is  to  put  science  and  Scripture 
together,  and  look  at  them  as  you  do  through  telescopic  glasses, 
till  the  two  views  blend  in  a  harmonious  unity,  and  proclaim  their 
common  authorship. 

"  '  Search  the  Scriptures '  is  the  law  of  His  Church  and  the 
talisman  of  His  bounty.  Let  us,  then,  no  longer  please  the 
devil  and  cramp  our  piety  by  neglecting  the  Bible.  Let  us  bring 
the  strength  of  our  being  to  the  careful  and  prayerful  exploration 
of  the  fertility  of  revelation,  where  grow  the  flowers  and  the 
fruits  of  Paradise.  Let  us  be  zealous  in  the  study  of  the  letter, 
that  we  may  reach  the  mind  of  the  Spirit.  Let  us  use  the  In- 
spired Word  as  the  medial  glass  through  which  we  may  the  more 
clearly  see  and  know  our  Lord  Jesus  Christ." 


3o6  Conclusion  to  Appendices.  §  97. 


CONCLUSION  TO  APPENDICES. 

Authorities  for  an  Esoteric  Reading  of  the  Bible. 

§  97.  As  is  seen,  the  great  display  of  the  creative  law 
of  measure  among  the  Egyptians  was  in  that  "  wonder  of 
the  world,'''  the  great  pyramid.  Among  the  Hebrews  it 
was  in  (i.)  the  Garden  of  Eden;  (2.)  the  Ark  of  Noah; 
(3.)  the  Tabernacle;  and  (4.)  the  Temple  of  Solomon. 
Around  these  actual  displays,  description  was  conveyed  by 
the  hieroglyphic  reading  of  the  narratives  of  the  Holy 
Writ.  "  Wo  be  to  the  man  who  says  that  the  Doctrine  de- 
livers common  stories  and  daily  words  !  For  if  this  were 
so,  then  we  also  in  our  time  could  compose  a  doctrine  in 
daily  words  which  would  deserve  far  more  praise.  If  it 
delivered  usual  words,  then  we  should  only  have  to  follow 
the  lawgivers  of  the  earth,  among  whom  we  find  far  loftier 
words  to  compose  a  doctrine.  Therefore,  we  must  believe 
that  every  word  of  the  Doctrine  contains  in  it  a  loftier  sense 
and  a  higher  meaning.  The  narratives  of  the  Doctrine 
are  its  cloak.  The  simple  look  onl}'-  at  the  garment — that 
is,  upon  the  narrative  of  the  Doctrine  ;  more  they  know 
not.  The  instructed,  however,  see  not  merely  the  cloak, 
but  what  the  cloak  covers."  (The  Sohar,  111,152;  Franck, 
119.)  So  the  Church:  "If  we  hold  to  the  letters,  and 
must  understand  what  stands  written  in  the  law  after  the 
manner  of  the  Jews  and  common  people,  then  I  should 
blush  to  confess  aloud  that  it  is  God  who  has  given  these 
laws  :  then  the  laws  of  men  appear  more  excellent  and 
reasonable."  (Origin,  Homil.  7,  in  Levit.)  "What  man 
of  sense  will  agree  with  the  statement  that  the  first,  second, 
and  third  days  in  which  the  evening  is  named,  and  the 
mortiing,  were  without  sun,  moon,  and  stars,  and  the  first 
day  without  a  heaven  ?  What  man  is  found  such  an  idiot 
as  to  suppose  that  God  planted  trees  in  Paradise,  in  Eden, 


§  98.  Conclusion  to  Appendices.  307 

like  a  husbandman,  etc.?  I  believe  that  every  man  must 
hold  these  things  for  images  under  which  a  hidden  sense 
lies  concealed."  (Origin  ;  Huet.  Originiana,  167  ;  Franck, 
121,  quoted  from  Sod.  "Genesis,"  p.  i75-)  "The  mys- 
teries OF  the  faith  not  to  be  divulged  to  all. 
But  since  this  tradition  is  not  published  alone  for  him  who 
perceives  the  magnificence  of  the  word,  it  is  requisite, 
therefore,  to  hide  in  a  mystery  the  wisdom  spoken,  which 
the  Son  of  God  taught."  (Clemens  Alexandrinus,  Strom. 
12.)  "  For  we  shall  find  that  very  many  of  the  dogmas 
that  are  held  by  such  sects  (of  barbarian  and  Hellenic  phi- 
losophy) as  have  not  become  utterly  senseless,  and  are  not 
cut  out  from  the  order  of  naitcre,''''  are  held  in  common 
with  us,  the  token  of  recognition  being  "by  cutting  ofi' 
Christ."  (Same,  Strom.  13.)  The  following  reflections 
and  notes  seem  appropriate  as  pointing  an  application  of 
these  statements  in  various  phases  of  a  same  system  ;  it 
being  premised  that  the  germ  or  key  of  all  these  hidden 
meanings  lay  in  the  possession  of  the  method  of  measure, 
and  in  the  measure  which  the  Lord  God  used  in  the  con- 
struction of  the  universe. 

The  Esoteric  Teaching  Confined  to  the  Few. 
§  98.  The  author  believes  that  no  man  can  study  the 
Bible  a  great  while,  carefully  and  dispassionately  noting 
its  place  in  the  world,  its  surroundings,  its  handings  down, 
its  prophetical  bearings,  not  considered  in  detail,  but  in 
their  large  and  comprehensive  scope,  without  coming  to 
the  conviction  that  a  Divine  power  and  providence  doth  in 
some  way  or  sort  hedge  it  about,  and  without  coming  to 
the  conviction  that  this  Divine  Power  is  a  conscious  entity, 
just  as  we  are  ;  that  He  is,  by  His  superiority,  wisdom, 
and  power,  continually  and  everywhere,  intelligently  pres- 
ent as  the  immediate  cause  of  each  sequence  in  all  the 
universe,  however  minute.  (Not  working  by  positive  fixed 
laws  of  construction,  which,  once  enacted,  the  work  can 
forever  go  on,  without  any  immediate  supervision  of  the 
Master,  a  postulate  so  commonly  assumed  ;  for  it  is  observ- 


3o8  Conclusion  to  Appendices.  §  98. 

able,  where  investigation  can  reach,  that  while  every  type 
of  work  seems  to  be  under  a  general  type  law,  yet  every 
individual  production  under  a  type  is  clearly  enough  seen 
to  be  a  variation  upon  every  other  individual,  thereby  ne- 
cessitating the  actual  intervention  of  creative  power  for 
every  individual  created  under  such  a  law.)  He  who  con- 
siders that  man  alone  is  the  only  phenomenon  in  all  the 
wide  universe  of  a  conscious  intelligence,  as  concreted 
from  an  infinite  number  of  blind  happenings  or  accidents, 
arrogates  very  much  to  the  superiority  of  his  accidental 
position,  especially  when  he  takes  into  view  his  own  ac- 
knowledged littleness  and  inferiority  ;  for  he  that  can  make 
nothing  is  yet  superior  to  the  blind  working  of  the  elements 
to  which  he  is  indebted  for  himself,  which  elements  come 
under  the  general  term  of  God  or  Nature.  What  a  pic- 
ture of  self-sufficiency  !  The  conscious  entity,  man,  simply 
proves  series  after  series  of  just  such  a  class  of  entities, 
graded  upward,  past  man's  power  of  recognition.  Man's 
ego,  as  connected,  even,  say,  inseparably  with  his  body,  is 
just  that  phenomenon  of  nature  that  implies  an  ego  func- 
tion of  nature  herself,  as  inseparably  connected  with  grosser 
material  than  that  function.  The  only  question  is  as  to 
whether,  in  man,  or  otherwise,  this  function  can  shed  its 
covering  for  another;  or  whether,  in  fact,  he  may  have 
two  kinds  of  material  body,  one  of  which  may  continue, 
the  other  perishing. 

But  apart  from  this,  and  as  to  the  Bible  this  being  said, 
there  are,  nevertheless,  some  strange  features  connected 
with  its  promulgation  and  condition.  Those  who  compiled 
this  Book  were  men  as  we  are.  They  knew,  saw,  handled, 
and  realized,  through  the  key  measure,  the  law  of  the 
living,  ever-active  God.  They  needed  no  faith  that  He  was, 
that  He  worked,  planned,  and  accomplished,  as  a  mighty 
mechanic  and  architect.  What  was  it,  then,  that  reserved 
to  them  alone  this  knowledge,  while,  first,  as  men  of  God, 
and  second,  as  apostles  of  Jesus  the  Christ,  they  doled  out 
a  blinding  ritual  service,  and  an  empty  teaching  oi  faith, 
and  no  substance  as  proof,  properly  coming  through  the 


§  99-  Conclusion  to  Appendices.  309 

exercise  of  just  those  senses  \vhich  the  Deity  has  given  all 
men  as  the  essential  means  of  obtaining  any  right  under- 
standing? Mystery,  and  parable,  and  dark  saying,  and 
cloaking  of  the  true  meanings  are  the  burdens  of  the  Tes- 
taments, Old  and  New.  Take  it  that  the  narratives  of  the 
Bible  were  purposed  inventions  to  deceive  the  ignorant 
masses,  even  while  enforcing  a  most  perfect  code  of  moral 
obligations  :  How  is  it  possible  to  justify  so  great  frauds, 
as  part  of  a  Divine  economy,  when  to  that  economy  the 
attribute  of  simple  and  perfect  truthfulness  must,  in  the 
nature  of  things,  be  ascribed  ?  What  has,  or  what  by  pos- 
sibility ought  myster}'-  to  have,  wiih  the  promulgation  of 
the  truths  of  God  ? 

Arc  the  Keys  of  this  Esotcrisin  Lost? 

§  99.  Men  like  ourselves,  who  were  capable  of  teaching 
the  multitudes,  held  this  knowledge,  both  in  the  times  of 
the  Old  and  of  the  New  Testament.  If  at  all,  when  was 
this  knowledge  lost?  There  is  witness,  by  the  emblems 
remaining  in  use,  that  two  modern  bodies  have  at  one  time 
been  in  possession  of  the  keys — viz.,  (i)  that  order  called 
the  Roman  Catholic  Church,  which  is  catholic  to  the  extent 
of  possession  of  the  emblems  of  the  universal  knowledge, 
which  was  confounded  by  tiie  confusion  of  lip,  and  which 
possession  has  been  dropped  by  all  sects,  creeds,  etc., 
which  have  dropped  the  consideration  of  the  basic  knowl- 
edge or  dahvar ;  and  (2)  that  body  of  men  called  Free 
Masons.  It  is  probable  that  the  Greek  Church,  and  the 
Brahmin  system  also,  come  under  this  category.  The 
elimination  of  the  vestiges  of  the  workings  by  the  key  sys- 
tem can  even  be  seen  in  the  English  Church  ;  for  one  of 
the  great  functions  of  the  church  was  to  regulate  the  order 
and  times  of  its  holidays.  This  was  done  agreeably  to  the 
passage  of  the  sun  in  his  circuits  through  the  signs  ;  but  in 
the  preparation  of  the  order  of  service,  as  it  is  to  be  seen 
on  the  origmal  rolls  (see  facsimile  of  the  Black  Letter 
Prayer-Book,  made  in  1663,  as  taken  from  the  original 
rolls  or  scrolls  in  the  British  archives),  it  was  deemed,  for 


3IO  Conclusion  to  Appendices.  §  99. 

some  reason,  best  to  wipe  out  those  calendars  teaching  the 
progress  of  the  sun  through  his  signs.  (There  is  but  little 
doubt  that  the  rules  for  the  calculation  of  tables  of  time, 
to  mark  the  proper  observance  of  religious  festivals,  which 
tables  are  prefixed  to  the  Book  of  Common  Prayer,  are 
precisely  the  same  to  be  found  in  the  first  chapters  of  Gen- 
esis, relating  to  the  founding  the  year  values  on  lunar  ta- 
bles. Christianity  is  almost  undoubtedly  indebted  to  the 
ancient  Jewish  and  Egyptian  calendar  rules,  on  which  she 
built  up  the  special  exceptional  details  of  her  own  forms.) 

Resolutions  of  the  Academy  of  Sciences  and  of  the  Royal 

Society. 
(i.)  One  of  the  most  remarkable  proofs  of  the  existence 
of  this  knowledge  (of  the  foundation  of  these  mysteries  on 
the  Parker  and  Metius  relations  of  circumference  to  diam- 
eter of  a  circle),  down  to  a  very  late  day,  lays,  as  it  would 
seem,  in  the  resolutions  passed  by  those  two  learned  bodies 
of  men,  the  Academy  of  Sciences  at  Paris  and  the  Royal 
Society  of  London.  (See  Parker's  Quadrature.)  It  was 
in  the  period  of  the  revival  of  knowledge,  when  the  world, 
possessed  of  extraordinary  intellects  and  wholly  athirst  for 
learning,  was  investigating  every  cranny  and  department 
of  nature.  All  recognized  the  fact  that  in  nature  one  of 
the  most  interesting  relations  was  that  of  circular  to  plane 
shape,  and  the  flux  of  one  into  the  other.  Ordinarily,  in 
matters  of  research,  promising  great  rewards,  none  so  per- 
sistently encouraging  of  interminable  effort  in  the  pursuit 
of  the  obscurer  realms  of  science  as  these  bodies.  What 
was  the  reason,  then,  that  on  the  production  by  Legendre 
of  his  acknowledgedly  approximate  value  of  tt,  the  Acad- 
emy of  Sciences  passed  that  famous  resolution  that  it  would 
never  entertain  any  thesis  on  the  subject  of  the  quadrature 
of  the  circle?  What  was  the  reason  that,  in  a  few  years 
afterward,  upon  Playfair's  following  in  the  footsteps  of 
Legendre,  the  Royal  Society  of  London  passed,  perhaps, 
a  copy  of  the  same  resolutions?  Since  that  time,  every 
man  daring  to  venture  into  that  forbidden  field  of  research 


§  99-  Conclusion  to  Appendices.  311 

has  been,  by  a  mysterious  common  consent,  hooted  down, 
laughed  at,  and  derided,  by  the  manifestations  of  a  mock- 
ing false  pity ;  and  just  in  the  measure  that  his  works  have 
proved  valuable,  just  in  that  measure  has  the  effort  been 
strong  to  remove  them  from  the  study  of  the  people.  Now, 
it  is  barely  possible  that  the  keys  of  these  old  mysteries  are 
still  known  and  held  by  very  few  ;  that  these  few  are  recog- 
nized by  the  very  highest  of  the  order,  so  that  an  order  to 
that  effect  of  procurement  of  just  such  a  piece  of  chicanery 
as  that  practiced  by  these  societies,  once  promulgated, 
would  be  obeyed  and  carried  into  effect  willingly,  and 
even  zealously,  by  multitudes  of  those  who  might  remain 
in  perfect  ignorance  as  to  the  source  of  the  order  or  as  to 
its  real  object. 

There  are,  moreover,  two  evidences  of  the  modern  ex- 
istence of  this  knowledge  in  symbolism. 

(2.)  In  "  The  Gnostics,"  Plate  VI.,  i,  is  to  be  found  a 
Templar  or  Rosicrucian  emblem.  It  is  of  that  "/c/o/,"  or 
'■'old  man,'''  a  worship  of  which  was  charged  against  the 
Templars.  It  is  of  an  old  man,  with  his  arms  crossed  in 
front.  At  his  feet,  on  one  side,  is  a  celestial  globe,  with  its 
subdivisions,  and  on  the  other  side  the  -pentapla,  or  five- 
pointed  star,  or  seal  oi  Solomon.  Here  are  displayed  the 
man,  113,  or  diameter  value  to  a  circumference  of  355,  or 
the  Hebrew  man,  the  celestial  circle,  and  the  fyrajuid. 
The  fcntapla,  as  it  is  drawn,  is  but  the  lined  display  of  a 
pyramid.  It  is  a  pentagon,  as  well  as  a  rayed  star.  Retain 
the  rays,  and  then  join  the  corners  by  lines,  and  the  object 


of  setting  forth  a  pyramid  is  at  once  apparent.  The  pyra- 
mid involves  all  the  measures,  with  the  purposes  thereof 
enumerated  in  the  text ;  so  the  whole  of  this  picture  symbol, 
though  modern  in  its  use,  really  disylaps  the  possession  of 


312  Conclusion  to  Appendices.  §  99. 

tlie   keys   of   the   ancient   knowledge   in   a  most   masterly 
manner. 

(3.)  In  '•'■  Land-Marks  of  Free  Masonry,^''  by  Oliver,  is 
to  be  found  a  frontispiece,  which,  for  magnificence  of  con- 
ception and  for  comprehensiveness  of  grasp,  is  most  re- 
markable. It  is  said  to  contain  the  symbolization  of  the 
genius  of  free  masonry,  and  is  said  to  have  been  designed 
by  Br.  Com.  J.  Harris,  P.  M.  and  P.  Z.  The  author  ven- 
tures to  state  positively  that  if  this  was  really  designed  by 
this  gentleman — that  is,  if  he  did  not  compile  it  from  simply 
traditionary  sources — then,  indeed,  he  must  have  been  ac- 
quainted with  the  elements  of  the  quadrature  as  John  A. 
Parker  has,  since  that  time,  set  them  forth,  their  astronom- 
ical application  in  architecture,  and  their  Biblical  contain- 
ment, in  a  fashion  of  such  wisdom  that  if  the  author  had 
possessed  it  in  its  details,  his  efforts  in  this  work  could  have 
been  relieved  of  suggestion.  The  reading  of  this  frontis- 
piece by  its  symbols,  even  with  the  imperfect  ability  of  the 
avithor,  is  always. a  source  of  exquisite  delight  and  unal- 
loyed amazement.  The  representation  is  in  a  rectangular 
oblong  of  tzvo  squares.  At  the  center  of  the  top  line  there 
is  located  the  triple  circle,  or  three  circles,  one  within  the 
other,  with  an  inclosed  triangle.  In  the  triangle  is  written 
the  Great  Name  m^T^  Reference  to  this  symbol,  §  82, 
will  show  that  it  exhibits  the  origin  of  vieasures^  in  the 
form  of  the  straight  line  one^  of  a  denomination  of  20612, 
the  only  numerical  value  of  the  perfect  circle,  the  straight 
line  being  male  and  the  circle  female,  as  the  ^  is  male  and 
the  TySTS  is  female  ;  which  20612  is  the  Logos,  or  Dahvar^ 
or  Word.  The  triangle  and  circles  indicate  the  pyramid 
containing  the  use  of  the  measures,  with  the  three  sets  of 
circular  elements  necessary  to  the  display  of  its  various 
problems.  This  emblem  is  in  an  effulgence  of  light,  above 
the  brightness  of  the  sun,  and  the  One  of  the  word  is  the 
holy  10,  and  circumference  to  318,  the  Gnostic  value  of 
Christ,  whence  this  spiritual  efTulgence.  From  this  upper 
essence  of  effulgence,  a  strong  bar  of  light  descends 
obliquely  to  the  foot  of  the  oblong.      On  the  one  side  of 


§  99-  Conclusion  to  Appendices.  313 

this  all  is  darkness,  and  chaos,  and  confusion,  containing 
darkness,  and  dragons,  and  all  deeps.  It  is  "Oa^  female  or 
sin  side.  At  the  foot  of  the  oblong  is  a  pavement  of  squared 
blocks,  in  cubes,  alternating  in  black  and  white  chequers, 
indicatincr  the  female  and  male  elements  of  construction ; 
and  on  the  dark  side,  this  pavement  is  not  made,  but  is  in 
confusion.  At  the  foot,  on  the  dark  side,  stands  a  little 
cherub,  striving  to  work  out  one  of  these  pavement  cubes 
from  a  rouijh  block  or  ashler,  but  without  success.  He 
stands  holding  his  chisel  and  hammer  in  a  helpless  sort  of 
way,  as  if  having  a  dim  idea  of  what  is  wanted,  but  as 
lacking  in  the  requisite  knowledge  for  elaboration.  The 
other  side  of  the  bar  of  light  is  bathed  in  the  essence  of 
wisdom  and  peace.  On  this  side  the  foot  has  a  completed 
pavement  of  the  black  and  white  chequers,  of  a  general 
oval,  indicating  the  measure  of  the  surface  of  the  earth. 
Just  opposite  the  discontented  cherub  is  seated  another,  but 
on  the  light  side.  He  is  looking  with  a  pleased  expression 
at  his  brother  in  the  obscurity.  His  right  arm  is  raised, 
and  he  is  pointing  with  \\\'&  forefinger,  the  rest  of  his  hand 
being  closed,  aloft  up  the  bar  of  light  to  its  source.  This 
forefinger  thus  pointing  is  the  symbol  of  the  Hebrew  jod,  % 
or  Jehovah,  orthe  number  10,  whose  origin  is  in  the  male- 
female  word  mn%  significant  of  the  same  number  as  ent- 
anating  from  the  deity  name  in  the  triangle  above.  His 
left  arm  is  thrown  over  as  embracing  two  parallel  upright 
bars,  inclosing  a  circle,  denoting  the  circle  in  the  square, 
the  measures  of  which  have  been  revealed  to  man  from 
above.  The  parallel  bars  are  supported  on  a  cube,  which 
is  one  of  the  cubes  of  the  pavement  raised  out  of  its  place 
to  the  level  of  the  floor,  and  the  upright  bars  are  but  the 
extension  of  the  sides  of  the  cube.  This  is  the  cubical 
stone,  and  the  square  of  the  bars  is  6561,  and  the  value  of 
the  circle  is  5153.  The  reading  is  instruction  on  the  part 
of  the  enlightened  cherub  to  his  brother,  telling  him  that 
from  the  geometrical  elements,  with  the  least  one  of  a  de- 
nomination of  20612,  located  aloft,  as  the  law  of  the  Deity, 
the  measures  of  work  have  been  revealed  to  man,  and  are 


314  Conclusion  to  Appendices.  §  100. 

under  his  control,  as  exhibited  in  the  circle,  the  square,  and 
the  cube ;  that  with  these  measures  the  cubical  blocks 
measuring  the  earth  are  to  be  formed.  In  this  is  the  lesson. 
The  oblong  then  contains  the  sun  and  the  moon  and  the 
stars,  as  further  being  measurable  by  man  through  this 
knowledge.  In  the  center  of  the  piece  there  flies,  or  hovers, 
a  female,  as  the  genius  of  the  whole.  Her  badge  is  on 
her  forehead,  and  it  is  the  fcntapla,  or  five  rayed  star, 
denoting,  as  shown  above,  the  pyramid  as  the  containment 
of  all  measures.  The  moon,  with  the  seven  planets,  repre- 
sent the  Garden  of  Eden  woman,  while  the  sun  denotes  the 
issuance  of  lunar  measures  in  terms  of  solar. 

All  this  condition  of  things  goes  to  show  that  the  mystery 
held,  as  not  to  be  thrown  open  to  the  people,  but  to  be  re- 
tained as  the  property  of  a  class,  and  a  caste,  in  the  more 
ancient  days,  may  never  have  passed  away  ;  but,  to  the 
contrary,  may  exist  even  to-day,  dominating  the  souls  of 
men,  women,  and  children,  by  keeping  them  in  perpetual 
ignorance,  and  in  religions  feeding  them  on  the  worn-out 
husks  of  faith,  without  any  relief,  by  way  of  setting  forth 
actual  connections  between  man  and  the  Deity. 

The  Province  of  Ritualism. 

§  100.  How  plainly  can  now  be  seen  the  origin  or 
source  and  reason  of  ritualism.  Ritualism  was  not  an 
empty  thing.  The  adoration  of  the  Deity  was  simply  a  con- 
stant reminder  of  man's  dependence  upon,  connection  with, 
and  knowledge  of  Him.  The  worship,  then,  was  the  ex- 
pression under  this  or  that  form,  by  gesture,  action,  signs, 
voice,  dress,  accompanied  by  visible  symbols  of  some  one 
or  more  of  the  exact  mathematical  formulations,  or  geomet- 
rical formulations,  or  numerical  combinations,  pertaining 
to  the  known  method  of  measuring  the  works  of  the  Deity. 
A  conclusion  of  Sir  William  Drummond  in  CEdipus  Ju- 
daicus  indirectly  favors  this  view  :  "  The  priests  of  Egypt 
and  of  Chaldea,"  he  says,  "  had  made  a  progress  in  the 
science  of  astronom}'',  which  will  be  found  more  astonishing 


§  loo.  Conclusion  to  Appendices.  315 

the  more  it  is  examined.  Their  cycles  were  calculated 
with  extraordinary  precision,  and  their  knowledge  of  the 
most  important  parts  of  astronomy  must  appear  evident  to 
all  who  candidly  consider  the  question.  But  the  people 
appear  to  have  been  purposely  left  in  gross  ignorance  on 
this  subject.  Their  vague  and  their  rural  years  were 
neither  of  them  correct.  The  festivals  were  fixed  accord- 
ing to  calendars  made  for  the  people,  and  the  religious  in- 
stitutions were  only  calculated  to  confirm  the  errors  of  the 
ignorant,  The  truths  of  science  were  the  arcana  of  the 
■priests^''  because  they  were  the  sources  of  religious  cultiis. 
Thus  ritualism  was  an  intelligible  rite,  one  to  be  under- 
stood in  all  its  parts  and  ramifications ;  one  in  which  there 
was  no  possible  deception  as  to  the  use  of  a  symbol,  to 
those  who  could  read  the  symbol.  No  danger  then,  or  at 
that  time,  of  paying  a  worship  to  the  thing.  A  carpenter 
might  as  easily  be  taught  to  fall  down  before  his  draw- 
knife  or  plane  as  a  religious  before  the  instruments  by 
which  he  copied  the  sums  of  his  Father  in  heaven.  In- 
trinsically, one  would  be  as  silly  and  fruitless  of  good  re- 
sults as  the  other.  It  has  been  the  gradual  and  finally 
almost  perfect  extinguishment  of  the  knowledge  of  the 
origin  of  ritualism  on  the  part  of  the  ^r/e5/5  themselves  that 
has  entailed  a  superstitious  use  on  the  part  of  the  laity. 

Ritualistic  Symbols. 

{a.)  One  of  the  most  prized  retentions  among  the  Jews 
of  religious  symbols  are  the  T^phillin.  They  stood  in 
place  of  the  cross  and  rosary  of  the  Christians.  They  are, 
in  fact,  but  the  means  of  exhibition  of  geometrical  and  nu- 
merical qualities  for  setting  forth  the  substance  of  Elohim, 
Shaddai,  or  Jehovah,  in  His  law  of  working.  One  of 
them  consists  of  a  flat  square  to  be  placed  on  the  forehead  ; 
on  this  is  a  cube,  lined  or  divided  oflf  into  four  divisions. 
It  is  the  Adam  or  Garden  of  Eden  square,  as  shown.  On 
one  side  of  this  cube  is  the  letter  C^,  with  three  prongs  ; 
on  the  other,  the  same  letter,  with  four  prongs,  the  3  and  4 
of  the  golden  candlestick,  of  the  cross,  and  of  the  Parker 


3i6  Conclusion  to  Appendices.  §  loo. 


problem;  which,  as  4^  =  i6 -^  3- =  9=  1777.77-f- ^  the 
pyramid  base,  as  to  its  circumference,  in  cubits.  This 
square  is  fastened  upon  the  head  by  a  band  permanently 
tied  behind  by  a  square  knot,  presenting  on  its  face  a 
square  face  of  a  cube  divided  into  four  parts,  as  noting  the 

8  small  cubes,  necessarily  going  to  make  up  a  next  larger 
one.  This  band  around  the  head  is  the  circle  pertaining 
to  the  square  and  cube,  with  the  quality  of  man  contained 
as  113,  the  circle  being  the  counterpart  311.  The  other  is 
a  similar  square,  with  a  simple  cube,  without  letters.  This 
is  to  be  fastened  on  the  left  and  bared  arm,  the  cube  being 
adjusted  over  the  heart ;  then  the  band  fastening  it  is  wound 
7  times  around  the  lower  or  fore-arm,  to  the  hand,  where 
it  is  so  interlaced  in  the  fingers  of  the  hand  as  to  form  the 
letter  £^,  or  Shaddai. 

As  simple  as  this  contrivance  is,  it  contains  the  elements 
of  a  pure  geometrical  and  numerical  system,  with  its  appli- 
cation as  a.system  of  measures  to  cosmical  or  God  uses.  The 
fore-arm  was  esteemed  to  be  th^  cubit  value,  or  yl^wwa?^ — 
that  is,  '-'■  viother  of  measures ;^''  and,  as  shown,  the  cubit 
indicates  the  Parker  value  20612,  source  of  the  Ddbvar  or 
Word.  The  wrapping  7  times  around  the  left  arm  was 
most  likely  the  serpent  of  the  Garden,  which,  as  the  letter 
D  (the  snake),  was  numerically  the  number  9,  the  inter- 
twined numbers  of  the  tree  of  the  Garden  as  i'^,  or  7  and 

9  (for  character  values).  The  noose  around  the  arm,  or 
the  upper  part  of  the  fore-arm,  represented  the  mouth  of 
the  serpent,  or  door  of  Indranee,  or  the  womb  of  time. 
The  word  Shaddai  is,  numerically,  either  by  adding  the 
letter  values,  simply  314,  or  a  circumference  to  a  diameter 
of  one,  or  else  by  adding  the  letters  (the  d,  because  of 
dagcsh,  being  doubled)  318,  or  a  diameter  to  a  circumfer- 
ence of  one ;  or,  by  giving  the  character  values  as  the  let- 
ters run,  381,  or  the  half  base  side  of  the  pyramid  (the  d 
doubled  by  dagcsh).  The  numbers  7  and  9  intertwined 
are  6t^,  or  counterparted  36 — St,,  which  are  of  Garden  of 
Eden  use. 

{p.)     Again,  as  to  the  cross  and  rosary,  at  the  same  time 


§  lOO.  Conclusion  to  Appendices.  317 

the  plainest,  simplest,  and  most  embracing  of  all  S3''mbols. 
The  cross  is  the  symbol  of  the  unfolding  of  the  cube,  which 
represented  the  perfect  circle  20612  taken  off  on  to  its  12 
edges,  the  man  on  it  representing  the  113  :  355,  or  Melius 
form.  The  rosary  is  a  string  of  bunches  of  beads.  There 
are  five  bunches  of  ten  beads  each,  making  50,  which  is 
the  letter  H,  or  5  raised  to  the  letter  J,  nun,  ox  fish,  or  niH, 
or  Eva.  Between  each  bunch  there  is  a  larger  bead  ;  of 
these  there  are  5,  which  is  the  letter  H;  or  the  productive 
womb-letter  of  the  Hebrews.  These  55  beads  close  the 
circle  as  the  distinctively  feminine  part.  But  the  circle  is 
only  looped  together  at  this  point ;  for  the  string  of  beads 
is  continued,  and  next  comes  a  bunch  of  three  beads,  as 
by  themselves,  then  a  large  bead ;  and  then  the  string  is 
terminated  by  the  cross  with  the  man  on  it.  The  3,  and 
then  55,  are  355.  Prefix  the  one  bead,  or  read  in  their 
order  of  bunching  together,  and  we  have  1355-  Bend  this 
into  the  form  of  a  circle,  and  we  have 

5       5 

3  I 
or  5135,  or  the  woman.  Place  the  Hebrew  letters,  and  add 
them,  and  there  results  311,  or  counterparted  311 — 113, 
the  man-woman  number.  Read  the  other  way,  and  there 
results  5153,  or  the  Parker  circle  inscribed  in  the  square  of 
6561,  as  to  which  5153  X  4=  206x2,  is  theZ^^^^z^^r  or  Word 
number.  In  short,  the  rosary  and  cross,  simply  in  this 
form,  represents  the  deepest  underlying  reading  of  the 
Garden  of  Eden,  and  thus  is  the  correct  representative 
symbol  of  the  entire  Old  Testament  ritual  and  knowledge. 
This  simply  shows  that  to  attack  the  ritual  of  the  Roman 
Church  to  the  extent  of  this  possession  is  simply  to  attack 
the  Bible  itself. 

How  desperately  blinding  becomes  a  superstitious  use, 
through  ignorance  of  such  emblems,  when  they  are  made 
to  possess  the  power  of  bloodshed  and  torture,  through  or- 
ders of  propaganda  of  any  species  of  religious  cultus. 
When  one  thinks  of  the  horrors  of  a  Moloeh,  or  Baal, 
or  Dagon  worship  ;  of  the  correlated  blood  deluges  under 


3i8  Conclusion  to  Appendices.  §  loo. 

the  cross  baptized  in  gore  by  Constantine,  as  the  initiative 
of  the  secular  church  ;  of  Jewish  faith  and  constancy, 
amidst  all  suffering,  the  dearest  treasure  left  by  way  of 
symbol  being  the  Cphillin; — when  one  thinks  of 'all  this, 
and  then  that  the  cause  of  all  has  been  simply  ignorance 
of  the  real  radical  reading  of  the  3foIoch,  and  Baal,  and 
Dagon,  and  the  cross,  and  the  fpkillin^  all  running  back 
to  a  common  origin,  and,  after  all,  being  nothing  more 
than  a  display  of  pure  and  natural  mathematics,  although 
and  albeit  of  a  Divine  foundation,  and  of  Deity  creative 
7ise,  one  is  apt  to  feel  like  cursing  ignorance,  and  to  lose 
confidence  in  what  are  called  intuitions  of  religion  :  one 
is  apt  to  wish  for  a  return  of  the  day  when  all  the  world 
was  of  one  lif  and  of  one  knowledge. 

The  exhibition  of  facts,  and  the  explanation  of  their  cor- 
relative uses,  in  this  work,  is  finished.  The  author  believes 
it  to  be  shown  that  the  elements  of  construction  of  the  pyr- 
amid, and  their  use,  agreeably  to  the  intention  of  the  ar- 
chitect, have  been  proved,  and  that  these  are  shown  to  be 
used  as  the  foundation  of  the  Bible  structure  from  the  first 
chapter  of  Genesis  to  the  closing  scenes  of  the  New  Tes- 
tament. But  while  these  elements  are  rational  and  scien- 
tific, and  in  the  Bible  rationally  and  scientifically  used,  let 
no  man  consider  that  with  this  discovery  comes  a  cutting 
off  of  the  spirituality  of  the  Bible  intention,  or  of  man's 
relation  to  this  spiritual  Ibundation.  Does  one  wish  to 
build  a  house  ?  No  house  was  ever  actually  built  with  tangi- 
ble material  until Jirst  the  architectural  design  of  building 
had  been  accomplished,  no  matter  whether  the  structure  was 
palace  or  hovel.  So  with  these  elements  and  numbers. 
They  are  not  of  man,  nor  are  they  of  his  invention.  They 
have  been  revealed  to  him  to  the  extent  of  his  ability  to 
realize  a  system,  which  is  the  creative  system,  o^  ihe.  eternal 
God ;  open  at  all  times  to  man  for  his  advance  into  its 
knowledge,  just  in  the  measure  of  his  application  and 
brain  abilit}'^ ;  free  to  all  as  is  the  water  we  drink  and  the 
air  we  breathe.     But,  spiritually,  to  man  the  value  of  this 


§  loo.  Conclusion  to  Appendices.  319 

matter  is,  that  he  can  actually,  in  contemplation,  bridge 
over  all  material  construction  of  the  cosmos,  and  pass  into 
the  very  thought  and  mind  of  God,  to  the  extent  of  recog- 
nizing this  system  of  design  for  cosmic  creation — yea,  even 
before  the  words  went  forth,  Let  there  he!  It  is  the  reali- 
zation of  the  existence  and  mental  workings  of  the  Divine 
mind,  by  means  of  the  little  primal  cube  and  its  circle, 
which  to  us  are  tangible  realities,  that  goes  to  prove  to  man 
that  his  soul  lives,  and  will  continue  to  live  ;  and  thus  he 
may  take  little  heed  for  his  body,  which  is,  however,  ex- 
quisitely constructed,  but  a  mask,  dulling  the  finer  powers 
of  his  mental  whole.  The  author  has  set  out  to  find  the 
truth.  To  the  extent  of  his  abihty,  let  hira  state  his  re- 
sults. The  best  and  most  authentic  vehicle  of  communica- 
tion from  God  to  man,  though  many  exist,  is  to  be  found  in 
the  Hebrew  Bible,  the  preservation  of  which,  in  its  exact- 
itudes, can  only  be  ascribed  to  a  spiritual  supervision.  But 
the  value  of  this  would  have  been  lost  had  it  not  been  for  a 
like  preservation  of  a  real  monument  of  the  practical  ap- 
plication of  the  Bible  secret.  This  monument  stands  to-day 
on  the  banks  of  the  Nile.  But,  by  turn,  this  also  would 
have  been  useless  to  man  had  there  not  been  a  ■preserva- 
tion of  the  actual  primal  measure,  which  has  been  shown 
to  be  the  British  inch.  Through  the  lapse  of  ages  this  has 
been  preserved  to  exactly  fit  to  the  solution  of  the  whole. 
None  but  a  spiritual  power  could  so  have  preserved  all 
these  means  of  restoration  of  the  ancient  (and  eternal) 
wisdom.  The  use  of  the  Biblical  method  of  display  of  the 
Divine  cosmogony  is  to  be  found  pure  and  truthful  in  some 
of  the  grandest  ritual  features  of  the  Roman  Catholic 
Church.  There  is  no  gainsaying  it,  for  it  is  so.  That 
church  uses  a  ritualistic  symbolization,  in  which  the  idea 
of  life  and  the  progression  of  life  predominates  ;  while, 
however,  it  has  been,  and  is,  perhaps,  in  possession  of  the 
more  radical  methods  of  disphw.  On  the  other  hand, 
Free  Masonry  holds  to  the  elemental  working  by  geomet- 
rical disTpVay — i.  e.,  by  the  harder,  more  exact,  and  purer 


320  Conclusion  to  Appendices.  §  loo. 

outlines  of  the  same  system  of  problems.  As  between  the 
two  systems,  in  thcindtimatc^  there  is  no  difference  at  all. 
Lord  God  of  a  common  humanity  !  loosen  the  shackles 
from  the  bodies  and  enlarge  the  souls  of  men.  Let  free- 
dom be  the  seed,  and  let  wisdom,  love,  peace — but,  above 
and  before  all,  charity — be  the  harvest.     And 

so    MOTE    IT    BE. 


ADDENDA.  32I 


ADDENDA. 


(A.)  (i.)  There  is  a  value  produced  so  beautifully,  and  yet 
so  curiously,  that  it  is  well  worthy  of  mention.  In  §  82,  on  page 
155,  the  elements  of  three  circles  are  given  as  springing  one  out 

of  the  other.     Of  these,  as  to  (3.)  its  height  is  to  its  —  base  side 

2 

(full  base  side  being  4S6,  the  standard  height  of  the  pyramid) 
as  309.3970502-I-  :  243  feet,  and  its  —  base  diagonal  is  343  653895 -[- 

feet,  or  4123.846740-}-   inches.     The  mode  of  procuring  this — 


base  diagonal  is  -  ^486^  X  2=  343-6538954-,  and  this  multi- 
plied by  12  =  4123.846740-!-  inches.  //  /s  seen  that  these  ele- 
ments are  derived  frotti  the  mass  ineasiires  of  the  pyramid^ 
"ivhich  are  derived  directly  from  the  Parker  forms. 

The  length  of  the  king's  chamber  is  sta^tdard  \\2Z.a^^  and  en- 
larged 4125.29396  tenths  of  inches.  Take  these  as  the  extremes 
to  find  a  mean  proportional,  and  we  have  4122.4  X  4125.29396-f- 
=  1 70061 1 1 82074-}-,  and  the  square  root  of  this  quotient  is  the 
7nean  proportional  required^  or  4123.8467-1-. 

So  it  is  seen  that  the  —  base  diagonal  of  pyramid   elements 

No.  3,  derived  from  the  mass  of  the  pyramid,  as  shown,  is  the 
mean  proportional  between  the  standard  and  enlarged  lengths  of 
the  king's  chamber ;  a  most  magnificent  result,  as  showing  the 

architectural  design,   one   may  say,  beyond    question.      This  — 

base  diagonal  value  is  exceedingly  close  on  to  the  radius  value  of 
the  circle  in  which  these  relations  are  shown,  for  that  radius  is  the 

—  of  the  sum  of  the  extremes,  and  the  —of  4122.4 -j-4125. 29396-}- 
2  2 

==:4i23.84698-f. 

Take  the  diagram,  page  138,  and  while  it  gives  the  general 
base  of  values  for  the  interior  works  of  the  pyramid,  it  is  also  the 
form  for  exhibition  of  the  two  lengths  of  the  king's  chamber;  for 


322  ADDENDA. 


AD  becomes 4 1 2.529396-1-5  D  B  becomes  412.24,  and  CD  becomes 
the  mean  proportional  between  these  extremes  of  412.3S467  ;  all 
to  a  radius  of  the  circle  412.3S469S-J-.  The  wonderful  value  of 
circular  elements  No.  3,  as  connecting  the  mass  of  the  pyramid 
with  the  interior  construction,  is  thus  clearly  unfolded  ;  and  it 
becomes  plain  why,  around  these  circular  elements,  in  4th  Gen- 
esis, it  is  found  that  so  many  of  the  prominent  Biblical  names 
{for  numbers)  concentrate. 

(2.)  Another,  but  symbolic  or  sympathetic  harmony,  can  be 
shown.  The  uses  of  the  pyramid  measures,  for  one  purpose,  are 
evidently  astronomical ;  and  while  the  symbolization  of  the  origin 
of  measures,  as  the  primal  one,  or  cube,  as  relates  to  pyramid 
construction,  is  set  forth  in  the  triple  circle  inclosing  the  pyramid 
and  \}i\Q.  great  name,  this  great  name  for  one  meaning  is  also  that 
of  the  pe7'J~ect  one,  pictured  as  a  circle,  with  a  diameter  drawn 
through  it,  as  the  year  circle.  But  this  year  circle  had  three 
values,  as  355,  360,  365  ;  wli^refore  this  symbol  may  be  taken 
also  as  expressive  of  these  three  year-circles,  containing,  as  they 
do,  the  Word ;  which  Word  is  expressive  of  the  year  circle,  and 
is  productive  of  all  things.  In  these  connections,  it  is  well 
enough  to  remark  that  the  letter  form  XX\7V  was  held  as  unpro- 
nounceable, because  it  was  in  fact  no  word  to  pronounce,  its 
meanings  being  held  in  symbols. 

(i?.)  It  is  seen  that  there  is  in  the  Hebrew  Bible  a  combina- 
tion of  the  pyramid  measure  elements  with  phallic  forms  and 
uses,  under  the  guise  of  the  man-wo/nan.  Is  not  this  combina- 
tion expressed  by  the  Sphinx  located  at  the  base  of  the  pyra- 
mid? The  author  has  seen  it  somewhere  stated,  as  a  reproach 
of  obscenity  against  the  ancient  Egyptians,  that  the  head  of 
the  Sphinx  is  disfigured  by  its  locks  of  hair  being  composed  of 
phallic  signs.  May  it  not  be  that  the  Sphinx  was  connected  with 
the  pyramid  as  part  of  its  reading.?  And  may  it  not  be  barely 
possible  that  there  is  some  passage-way  connecting  the  Sphinx 
with  the  interior  of  the  pyramid.?      (Suggested  by  a  friend.) 

(C)  The  Adam,  or  144,  relation  is  ihe  fufzdamenfal  one, 
carrying  the  pyramid  relations  into  the  Bible  ;  and  it  can  be  used 
by  scale.,  for  diflferent  proportions,  and  is  susceptible  of  any  kind 
of  scale  divisions  or  subdivisions ;  for  instance,  imder  the  devel- 
oping form  of  Arets,  Earth,  or  12,  it  is  12 2,  or  144,  giving  an 
area  value,  which  can  be  extended  by  use  of  the  factor  6  to  a 
larger  form,  while  as  144  it  may  be  used  as  a  line  on  which  a 
square  is  to  be  raised,  as  144 ■•^.     This,  as  inches,  gives  a  value 


ADDENDA.  323 


of  r3  in  jfect^  whereby  the  word  Arets^  earthy  or  12,  may  be 
taken  as  tlie  Adam  form  reduced  io  feet.  But  as  1442,  or  a 
square  of  144  to  the  edge  as  a  center  square,  then  this  enlarged 
to  jfour  squares  of  144  to  the  edge,  each,  gives  a  larger  square 
of  144  X  2  =  2SS  to  the  side,  or  2S8  X  4=  1152  (or  the  letters 
INRI,  as  numbers  1521,  read  in  a  circle.,  or  where  the  144^  (the 
interior  square)  is  subdivided  into  four  parts,  and  these  letters  are 
placed,  consecutively,  i  in  each  small  square  (rtiaterially  reading 
as  earth.,  air.,Jire,  and  water.,  the  containment  of  the  universe) ., 
these  can  be  read  as 

I        5 

I        2 

or  1 152),  the  circumference  of  the  larger  square.  But  in  inches 
288 -r-  12  =  z\  feet.,  and  this  represents  the  side  of  base  of  the 
pyramid.,  for  its  measure  is  diameter  to  a  circumference  of  2400 
(or  2\)  feet.  In  this  connection  it  is  observable  that  the  man- 
cross  and  triple-circle  Jehovah  symbols  are  essentially  the  same. 

(/?.)  It  is  altogetlier  probable  that  the  key  powe"  oUicraldric 
display  is  but  a  part  of,  and  a  vestige  of  this  ancient  system  of 
esotcrism. 

(Zi.)  The  three  motattains  in  one  to  the  top  of  which  Moses 
was  sent  up,  was  in  the  plains  of  Moab;  and  Aloab  may  be 
taken  as  a  sheet  ox  plain  of  water.  The  narrative  description 
may  be  changed  to  a  magnificent  picture.  The  lower  mountain 
of  the  three  was  Ibarif?z.,  or  Hebrews.,  or  heaven  dividers.,  or 
division  of  the  heavens.,  and  can  be  taken  as  the  subdivided  cir- 
cle of  360  degrees.  The  equivalent  of  this  circle  laying,  as  the 
base  of  Mt.  Ibarim,  on  \\\e.  face  of  the  waters.,  or  shimmering 
sea,  may  be  had  as  a  square.,  or  as  a  floating  ark.  Over  this 
let  the  brilliaiit  arch  of  the  sun  be  bent  as  a  bozv.,  which  is  Mt. 
Nebo,  as  including  the  wisdom  behind  the  sun;  and  let  this  be 
drawn  as  the  rainbow.,  showing  the  seven  primary  colors.  It  was 
on  the  summit  of  this  that  Moses  went  up  onto  the  reviewing 
.point.,  or  onto  Mt.  Pisgah.  He  may  be  taken  as  Enosh^  or  365 
—  I  =364,  or  Son  of  Alan.,  or,  again,  as  the  Holy  Spirit  of 
Wisdom  under  the  form  of  a  Dove  (used  in  the  flood  picture  as 
355 -f-5  =  yi)'"  This  is  a  second  termination  of  measures,  or 
power  of  measuring,  and  is  marked  by  the  recui'rence  of  the  ark 
floating  zipon  the  waters. 

(7^.)  Let  no  man  suffer  himself,  for  a  moment  even,  to  think 
that  the  correlative  likeness  of  the  Son  of  God,  the  manflre., 
fes-wa^  to  the  sun  in  the  heavens,  as  embracing  it,  is  in  any  wise 


324  ADDENDA. 


a  disparagement  to  the  Holy  Scriptures.  A  subtle  force  of  life 
is  traceable  through  grosser  material  forms,  in  what  we  call  the 
phenomenon  of  tnoiion^  which  becomes  manifested  in  the  ap- 
pearance of  Jirc ;  and  this  includes  what  we  call  electricity^ 
mag7zetisin^  mesmericni^  and  further  back  a  power  of  spiritual- 
ism. The  fire  of  the  sun  is  a  part  of  the  source  oi spiritual  life 
as  well  as  of  the  life  given  to  what  presents  itself  to  us  as  ma- 
terial. But  it  is  the  antagonism,  between  cold  and  Jire  {ox  dark- 
7tess  and  light).,  thi^ough  which  the  phenomena  of  the  tnodifi- 
cation  of  motion.,  or  of  life,  manifest  themselves.  Take  the 
earth  as  situated  at  a  certain  fixed  mean  limit  from  the  sun,  where 
it  is  balanced  between  the  effects  of  cold  and  heat.  Circular 
motion  on  its  axis  once  imparted  to  the  mass,  by  reason  of  the 
alternating  effects  of  cold  and  heat  on  this  mass,  not  only  will 
revolution  on  its  axis  continue  as  a  mechanical  result,  but  the 
pathway  of  the  eai"th  in  its  orbit  around  the  sun,  will  also  result 
as  a  concomitant  effect ;  and  this  will  (between  certain  extreme 
limits)  be  utilized  cosmically  by  more  subtle  mechanical  causes 
to  other  cosmical  effects.     (See  Force  in  Nature,  Section  IX.) 


SUPPLEMENT 


TO 


SOURCE  OF  MEASURES. 


SECTION    I. 

MEASURES. 

The  Egyptians,  Hebrews,  Romans,  and  probably  the  Hindoos, 
were  indebted  for  their  linear  measures  to  one  particular  measure 
which,  as  can  be  shown,  has  come  down  through  the  ages  unim- 
paired, viz., 

TTie  British  inch. 

This  measure  had  its  inception  in  the  numerical  integral  re- 
lation of 

Diameter  to  circuttiference  of  a  circle. 

The  area  of  a  square  of  8i  to  the  side  being  6561,  the  area  of 
the  circle  inscribed  in  that  square  is  5153  ;  and  by  a  simple  geo- 
metrical truism  the  diameter  of  a  circle  being  taken  as  6561,  its 
circumference  will  be  5153  X  4=  20612. 

All  these  measures  were  derived  from  this  formula  6561  : 
20612;  as  to  which  the  geometrical  relation  of  diameter  to  cir- 
cumference is  an  obedience. 

In  practical  application  of  these  numbers  on  a  measuring  stick 
or  rod,  they  were  attached  to  that  actual  measure  which  to-day  is 
styled   the    British   inch;    proved   by  the   standard  yard  measure 

(3) 


SUPPLEMENT.  TO    SOUPCE    OF    MEASURES. 


constructed  by  Captain  Kater,  in  the  year  1824,  from  the  British 
standard,  and  presented  by  the  British  government  to  the  magis- 
trates of  Edinburgh.  (Life  and  Works  at  the  Great  Pyramid, 
by  Piazzi  Smythe.) 

The  reason  why  the  value  of  the  British  inch  is  as  it  is,  is  be- 
cause it  was  just  that  value  which,  on  application,  would  make 
material  cosmic  magnitudes  correlate  with  the  times  and  distances 
of  the  planets  of  the  solar  system,  under  a  law  of  construction 
which,  by  the  ancients,  was  esteemed  to  be,  and  doubtless  was, 
divine. 

The  best  restorations  of  the  ancient  Egyptian  cubit  value  were 
those  made  by  Sir  Isaac  Newton,  from  many  measures  taken  of 
the  works  of  the  great  pyramid  of  Egypt  by  Professor  Greaves, 
of  Oxford,  England,  and  those  made  by  the  savans  of  the  French 
expedition  in  Egypt,  from  a  great  number  of  measures  taken  of 
the  rooms  and  passage-ways,  as  to  their  heights,  lengths,  and 
widths  of  the  catacombs  of  Osimandya. 

Sir  Isaac  Newton  (Smythe's  Life  and  Works)  found  this  re- 
stored value,  in  terms  of  the  British  foot  to  be 

1.7 1 7  feet. 

The  French  found  it  to  be,  in  terms  of  the  French  tfieter, 

.523524  77ieier. 

The  meter  \)€vcig  39.37079-1-  British  inches,  then  .523524  X  39- 

37079-}-  =  20. inches,   which,   divided    by   12,   gives    its 


value  in  British  feet,  as 

1. 7176294-  feet. 
Take  the  above  mentioned  circumference  value  as  20612  inches. 
Divide  it  by  12000,  and  there  results,  in  terms  of  British  feet, 

I. 717666+  feet  : 
and  this   shows  the   origin   of  the   ancient  cubit  value  as  derived 
(in  this  form  of  20612)  from  British  inches. 
If,  however,  we  take  the  form 

20612^       16     36643. 55-f- 

6561  )        9       1 1664. 


MEASURES. 


and  divide  this  raised  diameter  value  by  looo,  there  results: 

664 
II. — 

By  the  very  best  restorations  of  the  Roynan  foot  (see  as  to  the 

value  of  the  Roman  foot,  in  terms  of  British  measures,    "Great 

Pyramid,"  page  25,  by  Rev.  John  Taylor)  its  value  proves  to  be 

in  British   inches, 

664.     , 
II. —  mches', 

showing  a  common  origin. 

The  British  foot  of  12  inches  was  evidently  taken  as  the  recti- 
fication of  a  circumference  value  in  terms  of  the  above  formula, 
of  12  to  a  diameter  oi  3.819716-I-  feet. 

We  have  then — 

Diameter  6561 ;  circumference  20612. 

20612  _,..,.     ,  612  _,..,.     , 

British  inches,  or  20. —  British  inches, 

1000 

=  I  cubit. 

6561  X  16.     ,  664. 

— inches  ==^  11. —  inches, 

9000 

=  I  Roman  foot. 

•         1  •  r  8197164--         , 

12  inches  circumference  to  3. — inches  diameter, 

=  I  British  foot. 


SUPPLEMENT   TO    SOURCE    OF    MEASURES. 


SECTION    II. 

ARCHITECTURAL  DETAILS  OF  MEASURES  OF  THE  INTERIOR  OF  THE 
GREAT  PYRAMID  OF  EGYPT,  IN  TERMS  OF  THE  MEASURES  ESTAB- 
LISHED   IN    SECTION    I. 

The  forms  (of  circumference  to  diameter  of  a  circle),  viz  : 

20612   :  6561, 
utilized  in  value  as  British  inches,  were  the  basic  measures  used 
to  construct  this  pyramid  in  all  its  parts.     Take  the  forms, 
20612  is  to    6561 

47ooi-(- 
as  64800  IS  to  20626.--^ '- 

as  inches.     Divide  by  1000,  and  there  results: 

.    .  612  .  ^  561 

(i.)       20. —   IS  to    6.^^— 

,    .        ^    800  .              62647001  + 
(2.)  as  64. —  IS  to  20. 

612 
where  (i.),  20. —    inches  is    the  cubit  value,   as   a   circumference, 

62647  I 
and  in  (2.),  it  is  seen  that  a  dia/fieter  xAue  of  20. lilL  inches, 

approximates  very  closely  to  it.      Upon  these  two  forms  depended 

the  entire   construction   of  the   pyramid,   in  measures  of  inches, 

feet,   yards,    cubits,   miles;   of  days,   weeks,    months;    of  periods 

of  the  moon  and  of  the  earth ;  of  the  size  of  the   moon  and  of 

the  earth,  with  the  distance  to  the  sun,  as  springing  from  them. 

To  more  fully  appreciate  the  following  details,  which  are  to 
some  extent  supplementary  (especially  as  to  interpretation  of  use 
of  lines),  reference  is  made  to  Source  of  Measures,  by  the  au- 
thor. This  is  simply  a  development  from  the  grounds  and  meas- 
ures there  laid  down. 

The  height  of  pyramid  to  twice  its  base-side  has  the  propor- 
tion   of    diameter   to    circumference    of    a    circle.      20626.    '°°^ 


MEASURES   OF    INTERIOR    OF    GREAT    PYRAMID. 


(variation   on   20612),    2.%  feet  divided   by  27  =  763.943333980-}- 

47 -f- 
feet,  is  the  length  of  side  of  base.     This  is  the  same  as  20626. 

X — =36669.^-^^^^-^    inches,   equals    the    entire  circumference 

9 

of  the  iDase    of  the    pyramid;  or    for  the    base  side  in  feet  763.- 

943333980-!-  feet.     The   height,  therefore,    was   486. —   feet. 

As  to  the  pyramid  being  truncated,  see  Appendix. 

The  interior  works  were  referable  to  the  slope  line  of  the  ex- 
terior, to  the  base,  and  to  the  vertical  axial  line,  or  center  line,  of 
the  mass ;  therefore,  the  diagram,  annexed  hereto,  exhibiting  in 
vertical  section  the  half  of  the  structure,  is  sufficient  for  lengths 
and  heights. 

The  entrance  passage  as  to  the  center  of  its  floor,  longitudi- 
nally was  set  off  a  distance  to   the   eastward  of  the  center  of  the 

42190-1-  r         r  ■  •  ■  o 

base  side,  24.^^^ — - — ^feet,  for  reasons  given  in  section  7,  Source 

of  Measures — a  token  of  the  geometrical  origin  of  the  shape  of 
the  entire  mass. 

The  passage-ways,  as  to  their  dimensions,  are  constructed,  it 
would  seem,  on  mean  measures,  affording  a  very  small,  limited 
variation  of  values,  running  to  extremes  on  a  mean.  This  is  true 
also,  notably,  of  the  queen's  chamber,  whose  angles  at  the  cor- 
ners, as  shown  by  Piazzi  Smythe,  are  not  right  angles.  The 
lengths  of  the  passage-ways  afford  also  a  margin  (very  small  in- 
deed) over  and  above  a  mean  of  length.  Within  the  limits  of 
these  extremes,  by  very  nice  adjustment,  a  very  great  number  of 
comparative  and  correlating  measures  were  obtainable.  Ex- 
ample:    206.-^  inches  equal  10  cubits,  whereas  206. inches 

denote  a  diameter  to  a  circumference  of  648.  This  might  be  in 
a  scale  of  feet  for  inches,  though  as  a  fact  the  margin  of  differ- 
ence would  then  be  larger  than  is  the  fact.  The  margin  in 
inches  may  appear  in  tenths,  but  in  feet  it  would  likely  appear 
in  hundredths,  or  perhaps  thousandths.     This  feature  of  pyramid 


8  SUPPLEMENT   TO    SOURCE    OF    MEASURES. 


construction  is  shown  by  the  measures  of  Piazzi  Smythe,  which, 
it  may  be  said,  are  throughout  most  remarkable  for  their  exacti- 
tude. 

SPECIFICATIONS. 

(i.)  The  pyramid  is  based  on  a  pavement  which  is  intcluded  in 

6t  2 

the  mass  of  the  structure.     Its  thickness  is  20. —    inches,  or  one 

7  i't5-|- 
cubit,  or  i.^^— ^ — —  feet. 

This  is  a  circumference  to  a  diameter  of  6.  ^ —  inches. 

(2.)  Line  aa}-  is  the  one-half  base  side  of  pyramid,  and  equals 

47001+  16 

m  length  20626.  inches  X  —  equals  381.971666990  feet. 

12  72 

or     III. cubits,    or    4583.660003880-I-    inches.       Actual 

measure  by  Howard  Vyse,  382.  feet;  difference  .02  of  a  foot. 

Note.   381.       "'"  x  equals  the  length  of  the  king's  cham- 


200 


ber  in  feet.  Also  this  distance  is  diameter  to  a  circumference 
of  1200  feet,  or  14400  inches,  or  area  of  one  square  foot  multi- 
plied by  100  ;  or,  as  minutes,  it  equals  10  days  in  time  measure. 

(3.)  Line  a^  c  is  the  vertical  height,  above  the  base  of  the 
pyramid,  of  the  point  of  intersection  of  the  floor  line  of  the  de- 
scending passage-way  with  slope  line  of  the   structure.     Its  length 

is  31  cubits,  or  20. —  x  31  =  638.—  inches,  equal  to  53.-^^— 
feet.  The  same  measure  computed  by  Howard  Vyse,  53.1975 
feet  (Source  of  Measures,  p.  119).  The  line  a  c  to  the  foot  of 
this  line  is  41.820641  II i-f-  feet,  or  501.847693334- inches.  These 
lines  are  in  the  following  proportions  to  each  other  :  a^  c  :  a  c  :  : 
6561  :  5153,  or  as  the  area  of  the  square  of  81  is  to  that  of  its  in- 
scribed circle.  In  the  scale  of  inches  for  feet,  they  very  nearly 
represent  the   relation   of  vertical   height  of  descending    passage- 


MEASURES    OF    INTERIOR    OF    GREAT    I'YRAMID.  9 

way  to  its  breadth,  so  much  so  as  to  proportion,  that  these  given, 
viz.,  6561  :  5153,  may  be  taken   as  a  guide  for  the  dimensions  of 
that  passage. 

Note.  The  height  values  of  thie  descending  passage-way  as  taken  (7.), 
are  height  vertical  to  horizon  52.7S95656+  inches,  and  the  perpendicular 
to  the  incline  of  the  passage  47.25419656+  inches.  By  using  the  propor- 
tion given,  to  find  the  breadth  we  have  6561  :  5153  :  52.7895+  :  41.- 
460849+  inches  for  breadth  of  passage;  or,  for  dimensions  of  descending 
passage-way  we  have — 

Height  vertical,  52.7895656+    inches. 

"       perpendicular  to  incline,     47.25419656+       " 
Breadth,  41.460849+ 

The  dimensions  of  this  passage-way  may  show  a  change  of  values  on 
these,  by  the  biased  construction  of  its  sides,  and  top  and  bottom,  of: 

^18700722  ^        ,     /     ,  r 

(a.)   For  vertical  height  take  - — ^^^^ — =53.051620+  (where  31.8309722 

is  diameter  to  a  circumference  of  100):  then  we  will  have  as  a  variation — 

Height  vertical,  53.051620      inches. 

*'       perpendicular  to  incline.         47.488772+       " 

Breadth,  41.666666+ 

714.1 C9426  ,    ,     ,  , 

[b.)   For  vertical  height  take  ,        -  =  52.359904+  (where  314.159426 

is  circumference  to  a  diameter  of  100):  then  we  will  have  as  a  variation — 
Height  vertical,  52.359904+    inches. 

"       perpendicular  to  incline,       46.8695884+       " 

Breadth,  41,1233939+        " 

Suppose  the  arithmetical  mean  of  {a)  and  [b.)  is  used,  as — 

Height  vertical,  52.70576+  inches. 

"       perpendicular  to  incline,  47.17918+       " 

Breadth,  41.39502+       " 

now  the  measures  of  Piazzi  Smythe  show  a  much  greater  limit  of  accom- 
modation than  here  required. 

The  line  «"  aS  is  shown  to  be  (8.),  251.71412+  feet;  or,  numerically,  tl\e 
square  root  oi  one  mile  in  inches.  ^^251.71412+ =501.7111953,  and  this 
is  a  very  slight  variation  on  the  value  a  c,  or  501.S476+  inches.  So,  also, 
the  line  /'  d,  see  diagram  of  part  of  descending  passage-way,  is  14.842233+ 
inches;  this  divided  by  12=  1.23685+  feet;  showing  a  very  close  agree- 
•ment  with  the  floor  line  of  the  ascending  passage-way,  proportionally, 
that  line  being  123.6830+  feet. 


lO  SUPPLEMENT    TO    SOURCE    OF  MEASURES. 

(4.)  Line  a'' aMs  the  ^it;^r  line  of  the  descending  passage-way, 

,   .           62647001 -j-    .     ,  , 

and  IS  20. inches  X  200,  equal  to  41 25. 2 94003493 -f- 

inches,    or   343.774500291-1-    feet.       Same    measure    by    Howard 

Vyse  "  about  4126  "  inches. 

Note.  This,  as  seen,  is  a  diameter  line,  and  gives  a  circum- 
ference of  1080    feet,    or    12960   inches,    or'  10    times   ojie  square 

yard,  or  —   of  one  solar  day. 
400 

The  length  of  this  line  is  10  times  the  length  of  the  king's 
chamber.  The  Hne  ^  ^' equals  100  feet,  or  1200  inches.  Com- 
pare with  (2.)  "  Note." 

(5.)  Line  a^  c^  is  the  distance  from  the  floor  line  of  the  de- 
scending passage-way  to  the  vertical  axial  line  of  the  pyramid. 
Its  length  is  32.4237769849+  feet,  or  3890.853238188+  inches,  or 
18.87664+  cubits. 

Note.  Though  this  distance  may  be  relied  on  as  architectur- 
ally correct,  no  interpretation  can  be  given  of  the  line.  As  a 
whole,  it  is  cut  by  the  wall  of  the  subterranean  chamber. 

(6.)  The  key  to  the  works  above  the  descending  passage-way 
rests  in  the  value  of  the  line  b  d,  or  on  the  perpendicular  let  fall 
from  the  roof  line  on  to  the  floor  of  the  horizontal  passage-way. 
The  line  a^  b  is  parallel  to  the  exterior  slope  line  of  the  structure. 

The  length  of  this  line  ^^is  3.16227766+  feet,  or  37.94733192  + 
inches. 

Note.      The    interpretation    of  this    line    is    very    remarkable. 
Form  o(  circumference  to  diameter  is  20612  :  6561  as  said. 
Circumference   to    a    diameter   of    i    foot,    is   3. 141 594269+    feet. 
Diameter  to  a  circumference  of  10   feet,    is  3.1830972249+    feet. 
The  mean  proportional  htiweevx  these  values  is  (as  stated), 

3. 16227766+  feet. 
Now  this  last   value    is    the  square   root  of   lo :    in    inches,    as 
37-94733192  +  ,  it  is  the  square  root  of 

1440  inches. 


MEASURES    OF    INTERIOR    OF    GREAT    PYRAMID.  II 


The  half  base  side  of  the  pyramid  (2.),  is  seen  to  be  a  diam- 
eter to  a  circumference  of 

14400  inches. 
Thus  the  relation  becomes  manifest.      But  as  the  half  base  side 

equals ■  of  the  length  of  the  king's  chamber,  connection  with 

that  is  shown.  And  as  the  length  of  the  descending  passage-way 
is  shown  (4.)  to  be  10  times  the  length  of  the  king's  chamber, 
connection  with  that  is  shown.  Therefore  all  of  them  are  con- 
nected with  the  square  of  12  inches,  or  144,  both  as  a  linear  meas- 
ure and  a  measure  of  time,  because  1440  is  the  minutes  in  24 
hours.  For  an  immediate  check  upon  this  value,  the  dimensions 
of  the  descending  passage-way  are  now  given. 

(7.)  From  the  data  in  (6.)  the  height  of  the  descending  passage- 
way, perpendicular  to  its  inclim^  will  be 

47.25419656-}-  inches. 
Piazzi  Smythe's  measure  of  the  same,  as  per  his  tables  of  ac- 
tual measure, 

47.24  inches. 
Difference : 

.014  of  an  inch. 
Its  vertical  height  will  be 

52.78956568-}-  inches. 

Note.  At  the  foot  of  the  descending  passage-way  in  actual 
construction,  as  per  Howard  Vyse,  the  mason  work  is  set  back 
and  down  as  indicated  by  the  dotted  lines  (also  see  Perring's 
Plates),  so  that  the  actual  vertical  height  of  the  passage  to  the 
subterranean  chamber  is  contracted  or  reduced  from  the  descend- 
ing passage  way,  to 

3  feet, 
or 

36  inches; 
which  accords  again  with  contents  of  note   to    (6.),  because   36 


12  SUPPLEMENT    TO    SOURCE   OF    MEASURES. 

inches  is  i  yard.     Its  area  is  36^  or  1296  inches,  and  1296  X  4  = 

"5184,  the of  I   solar  day;  thus  making  the  yard  numerically 

1000 

a  base  for  the  correlation  of  distance  and  time  measures. 

(8.)  The  Une  a*'  a^  extending  from  the  intersection  of  the  roof 
line  of  the  descending,  with  the  floor  line  of  the  ascending  pas- 
sage-way to  the  vertical  axial  line  of  the  pyramid,  is  the  base 
line  of  construction  of  all  the  upper  works. 

Its  value  is 

251.714123560+  feet, 
or 

3020. 569482 7 -|-  inches. 

Note.     The  interpretation  of  this  line  is,  that  it  is  the  square 

root  of 

63360, 

which,    as   inches    (by    scale),    is    just    the    value    of    one   mile   in 

British  measure,  or 

5280  feet. 

So  that,  all  the  upper  works  embraced   between   the   Hnes  a*-  a^ 

and  the  vertical  axial  line  of  the  pyramid,  viz. ,  a^  a^,  are  included 

in  a  square  area  denoting  i   mile  British.     As  a  check   on   this 

line,  Howard  Vyse  gives  the  line  a*  b  as  247.7  ^^et.  It  is  247.- 
75265939+  feet.  Difference  .05  of  a  foot.  But  the  accuracy  of 
this  line  is  checked  back,  again  and  again,  by  the  coming  to- 
gether of  all  the  lines  of  the  upper  works. 

(9.)     The  consideration  of  the  contents  of  (8.),  leads  first  to  the 

measure  of  the  line  a^  a*.     This  line  is  in  length 

137.5098001 1 64-f-  feet, 
or 

1650.1176013968-I-  inches. 

Note.  This  line  is  4  times  the  length  of  the  king's  chamber. 
Its  main  interpretation  is,  that  as  inches  it  is  a  diameter  to  a  cir- 
cumference of   5184  inches,   or  the  number  of  inches  in  4  square 

yards,  or  the  exact  value  of  the  of  one    solar   day    in   thirds. 

-^  1000 

The  connection  between  this  line  and  «*  a^,  noted  in  (8.),  is  re- 


MEASURES    OF    INTERIOR    OF    GREAT    PYRAMID.  I3 


markable.  The  extremes  of  the  British  long  measures  are  the 
inch  and  the  viile,  or,  say,  the  cubic  foot  of  12  inches,  and  the 
cubic  mile.  Then  12^  and  5280'  represent  these  extremes.  Per- 
forming the  operation  we  have 

1728  and   147197952000. 
Dividing  the  one  by  the  other,  we  have  a  quotient  of 

85184000. 
Dividmg  by  80000000,   and  we   have  a  quotient  of  i,  with  a  re- 
mainder over  of 

5184000, 

which,  as  thirds,  is  just  one  solar  day.  That  this  value  thus 
found  was  used  for  this  showing,  to  connect  the  line  a^  a^,  with 
a^  a®,  which  last  as  seen  is  a  diameter  to  a  circumference  of  5184, 
seems  positively  to  have  been  the  case  to  the  author.  It  does  not 
seem  that  by  the  system  of  the  ancients,  our  method  of  multipli- 
cation and  division  was  used,  but  rather  addition  and  subtraction. 
In  this  view,  having  the  value  5280^ -r-  12^  as  seen,  the  use  would 

have  been 

85184000 

less  80000000 


Remainder,    5184000 
or  I  solar  day  value  thus  arising.     Their  method  of  use  is  yet  to 
be  discovered ;  but  an  example  of  a  like  use  to  get  the  value  of  a 
line  is  shown  in  (10.). 

Of  this  line,  for  verification,  reference  is  made  to  Source  of 
Measures,  where,  not  at  that  time  being  able  to  interpret  any  lines 
connected  with    the  roof  line  of  the  ascending   passage-way,   but 

simply  working  with  the  forms   20612   and   20626. as  nearly 

in  harmony  with  the  found  measures  as  possible,  making  a  posi- 
tively dependent  use  of  Piazzi  Smythe's  measures  as  regards  that 
roof  line  and  the  upper  works,  the  author  arrived  at  the  deter- 
mination of  this  line  to  within  so  small  an  amount,  viz.,  .0095  of 
a  foot  (see  page  136),  that  he  at  once  accepted  of  this  value  as 
without  doubt,  the  true  one.     No  attempt  was  there  made  at  in- 


14  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 


termediate  exactitudes,  from  inability  at  that  time  to  interpret  any 
meanings  of  lines  which  would  serve  as  a  guide  to  work  back 
and  forth,  checking  results  by  the  harmonies  of  relations. 

(lo.)  The  line  a^  d\  embraced  between  the  north  wall  of  the 

grand  gallery  and  the   north  wall  of  the  queen's  chamber,  comes 

next  in  order.     Add  to  itself,   as  inches,   the   ^   of  206.12;  or, 

206.12+103.06  =  309.18.      Add  to  itself,  as  inches,  the    1/3  of 

2647001+               ,  2647001+   ,  \x2X^Qo  ■?Q7oc:oi  + 

206. — — -^  ;  or,  206. — ^-^ L  +103,-^^-^^— —309.^^^-^-^— -^ 

inches.     Subtract  one  sum  for  the  other,  or, 

3970501+  i8 

309. 309. —  ^=.2170501  of  an  inch. 

Raise  this  by  1000  times,  it  equals 

217.0501  inches. 

Multiply  this  product  by  7,  or, 

217.0501  X  7  =  1519.3507  inches. 

This  is  the  measure  of  the  line  «"</':  and  it  is  very  observable 

as  being  a  difference  founded  on   10  cubits  and  its  enlargement, 

or  the   difference    between   the  width,    north  and  south,   of    the 

queen's  chamber,  to  which  the  line  leads,  which  is  10  cubits,  and 

the  width,   north  and  south,  of  the  king's  chamber,  which  is  the 

I                                  , •      ^     ,  12  .     ,     .              ^  2647001    .     , 
enlargement  on  10  cubits  (206. —  inches),  or  206.—-^-^ inches. 

Piazzi  Smythe's  measure  of  this  line  is  1519.4  inches;  differ- 
ence, .0493  of  an  inch.  As  another  verification  of  this  use,  he 
found  that  the  line  was  a  multiple  of  217  by  7. 

(11.)  The  line  d^  a\  or  the  width  of  the  queen's  chamber, 
north  and  south,  is 

206. —  inches, 
or,  10  cubits. 

Piazzi  Smythe  gives  for  this  measure,  four  measures;  two 
taken  on  the  east  side  of  the  room,  and  two  on  the  west  side; 
taken  at  two  separate  times.  East  side,  204.7,  206.5;  ^^^st  side, 
206.3,  205.6.  The  taken  measure,  which  is  typical  and  in  gen- 
eral harmony,  will,  however,  verify  itself  as  correct.     But  bear  in 


MEASURES    OF    INTERIOR    OF    GREAT    PYRAMID.  15 


mind  that  this  chamber  affords  extremes  of  measures  taken  on  a 
mean. 

(12.)  The  line  «*  a^,  being  the  floor  line  of  the  grand  gallery, 
intersecting  the  vertical  axial  line  of  the  pyramid  at  a*,  is 

156.8744966-!-  feet. 
This  measure  is 

91.—  cubits. 
Piazzi  Smythe  gives  this  line  as  156.9  feet:  difference,   .025  of 
a  foot. 

(13.)  Having  this  line  with  a^  d^  and  d^  a\  as  given  in  (10.) 
and  (ii.),  we  can  determine  the  line  c'^  a^ :  and  also,  which  is  a 
matter  of  the  greatest  moment,  where  the  vertical  axial  line  of  the 
pyramid  cuts  the  floor  length  (north  and  south)  of  the  queen's 
chamber. 

(i.)  c'  a^  is  found  to  be 

69.48255243+  feet. 

(2.)  It  is  found  that  the  length  c'  a\  of  the  floor  line  of  the 
queen's  chamber,  lays  to  the  south  of  the  vertical  axial  line  of  the 
pyramid,  and  its  value  is  found  to  be 

3.14159426+  feet; 
or,    cinumferance  to  a  diameter  of   i   foot ;    or,   it    is  the  circum- 
ference   to  a   circle,    inclosed  in    the   area   of  one   square  foot,    or 

144  inches,    or    the  —  part  of    one    solar  day  in  minutes,   or  the 

ID 

other  extreme  of  the  British  measures  from  the  line  a*  a^,  which, 
as  seen,  is  the  square  root  of  one  mile  as  63360  inches. 

(14.)  We    can    now  work  back    to    ascertain    the  value  of  the 

line  a*  a",  which  is  the  length  of  the  floor  line  of  the  ascending 

passage.      From   the  above  data,   as  ascertained,  its  value  proves 

to  be 

123.68300698+  feet. 

Piazzi  Smythe  makes  it 

123.683  feet: 

difference,   one  may  say,   nothing.      20.612  X  6  =  123.672,  show- 


l6  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 

ing,  in  inches  for  feet,  this  value  as  modified  on  the  typical  form. 
Or,  also,  123.68300698-f-  feet  are  72.00-I-  cubits. 

(15.)   Reverting    now   to    the    queen's    chamber,   d^   a'   equals 

206. —    inches,    or    17. ~^-  feet,    or    10    cubits,     c^   a'   equals 

3.14159426+  feet,   or   37.699131 12-|-  inches.     Then  d^  c^  must 
equal 


168.42086888+  inches. 


or 


14-03507240-1-  feet. 

(i.)  The  part  d^  c^,  thus  found,  governs  the  height  of  the  walls 

of  the  room,  as  ^'  d''  above  (vertically)  the  point  a^,  or  the  line 

a^  a' ;  making  this  height,  with  the   length  d^  c^,  a  perfect  square. 

This  height,  therefore,  is 

168.42086888+  inches. 

d^  0  \.o  the  floor  is  given  by  Piazzi  Smythe  as 

14  inches. 
Sum, 

182.42086888+  inches. 

Piazzi  Smythe  measured  this  full  line  as 

182.4  inches: 
difference, 

.02  of  an  inch. 

(2.)  The  value  of  the  solar  day,  in  thirds,  is 

5184000'" 

The  value  of  one  sidereal  day  is 

5169846'" 

Take  these  values  as  represented  by 

184  ^ 
5.—^  feet, 

and 

169846  . 
5.  feet, 

or,  in  inches, 

62.208  inches, 
and 

62.038152  inches. 

The    line  m  n,   or  the    height    of  the  gable,    is  thought  to  rep- 
resent either  one  or  both  of  these  values;  if  the  latter,  then  by  a 


MEASURES    OF    INTERIOR    OF    GREAT    PYRAMID.  17 

bias   on  the   roof  line    of  this   gable.      Piazzi    Smythe    gives    this 

distance  as 

62.  inches. 

But,   by  correcting  his  computed  measure  of  the  floor  line  as  205.8 

to  206.12,  his  value  would  have  been  62.2  inches. 

There  results  therefore,  for  greatest  height,       62.208  inches. 

168.420      " 

14. 


Sum,  244.628  inches, 

or,  244.428      " 

Piazzi  Smythe  makes  the  full  height,  244.4  " 


Difference,  .028  inches. 

Note,  (a.)  Considering  the  location  of  the  queen's  chamber,  in  its  east 
and  ivest  length,  with  reference  to  the  vertical  axial  line  of  the  pyramid.  In 
Source  of  Measures,  page  126,  it  is  stated  that  the  center  longitudinal  line 
of  the  floor  of  the  descending  passage-waj  is  set  off  to  the  eastward  of  the 
vertical  axial  line  of  the  pyramid 

24.42190  feet, 
or,  293.06280  inches. 

Take  now  the  length  of  the  line  a*  a^,  or,  251.7141235+  feet,  as  inches^ 

251.7141235+  inches. 
Add  a  sidereal  day  as  taken,     62.038152  " 


Sum,  313-752275  inches. 

Deduct  from  above,  293.06280         " 


Difference,  20.68947  inches. 

Which  gives  the  ^  width  of  the  passage-way  to  the  queen's 

chamber.     Its  full  width  would  be  41.37894  inches. 

Making  use  of  a  solar  day,  instead  of  a  sidereal  day,  and 

this  result  would  become  41.61864       " 

The  mean  of  these  values  is  41.4987         " 

Piazzi    Smythe's  measure  of  the  width  of  this  particular 

passage-way,  immediately  at   the   door   of  the   queen's 

chamber,  is  4146  " 

Difference,  .04  •* 


1 8  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 

il>.)  Take  the  values  found  above  of  the  distances  from  the  center  line 
of  the  pyramid  to  the  cast  wall  of  the  queen's  chamber,  made  up  (i.)  by 
the  mile  value  in  inches  with  the  value  of  a  sidereal  day  in  inches,  viz., 

313752275  inches. 
Divide  by  2,  and  we  have  156.S76137      " 

And  this  shows  that  the  value  of  the  floor  line  of  the  grand  gallery,  or 
the  line  a^  a^,  wliich  has  been  seen  to  be 

I56.S7449  feet, 
has  its  origin  here  in  this  queen's  chamber,  as  worked  in  a  scale  of  inches 
for  feet.     The  difference  is  .0016  inch. 

We  must  not  lose  sight  of  the  fact,  that  all  the  lines  are  on  a  bias,  or, 
give  extremes  on  a  mean  of  measures,  to  accommodate  to  a  variety  of 
correlating  measures. 

(c.)  From  considerations  of  widths  of  passage-ways  not  shown  on  this 
diagram  [but  see  Source  of  Measures,  page  127  («.),  (i.)],  the  extreme 
width  of  the  passage-wa\'s,  on  the  mean,  is  taken  at  41.6666+  inches. 

The  mean,  founded  on  the  data  given    in    note    (3.),    is 

taken  at  41.460S49      " 

The  least  extreme  then,  if  used  at  all,  would  be  41.265503      " 

(Although  all  these  measures  are  founded  on  data  fully  in  accord  with 
the  spirit  of  this  inquiry,  they  lack  for  that  kind  of  support,  given  in  all 
the  other  lines;  in  other  words,  they  lack  for  interpretation.) 

A  verj'  striking  datum  of  width  of  passage-ways,  as  to  what  their 
greatest  extreme  is,  is  had  in  Piazzi  Smj-the's  measure  of  the  width  of  the 
granite  portcullis  block  in  the  mouth  of  the  ascending  passage-way.  He 
gives  its  measure  of  breadth  at  41.6    inches. 

Dift'erence  between  this  and  the  extreme  taken,  .03       " 

(</.)  Now,  taking  the  passage  way  to  the  queen's  chamber,  by  means  of 
biased  lines,  to  indicate  a  permissible  limit  between  41.6666-f-  and  41.46-)- 
inches,  as  to  outside  limits,  the  following  data  are  derivable  as  to  the  east 
and  west  lengths  of  this  room,  as  they  have  relation  to  the  vertical  plane 
parallel  to  these  walls  cutting  through  the  axial  line. 

(i.)  Take  the  distance  of  center  of  passage-way  from  the  center  of  the 

pyramid  as  above,  293.06280-I-  inches. 

.   ,  ,  .  /      .  ,  ,      ^                  41 .66666 
Add  Yz  width  of  passage, =  20.83333-f-      " 


Sum,  313.89613      inches. 

Deduct  20.612  X  2=  41.224  " 

(a.)  Difference,  272.67213      inches. 


MEASURES    OF    INTERIOR    OF    GREAT    PYRAMID.  19 


Take  length  of  queen's  •chamber  at  226.21001       inches. 

Deduct  2Q.612  X  -  =  41.224  " 


{b.)  DiflTerence,  184.9S601      inches. 

From  (a.)  272.67213 

Deduct  {b.)  184.98601 


Remainder,  87.6S612      inches. 

From  this  deduct  "^  .20612  " 


Remainder,  87.48  inches. 

Showing  that  the  distance  from  the  west  wall  of  the 
queen's  chamber  to  the  plane  of  the  vertical  axial 
line  is,  numerically,  87.4S 

Plus  .20612 


Now,  as  to  these,  20612  is  our  tvpical  source  of  measures;  and  = 


5 1  S3. 

was  astronoinically  used  as of  one  circular  day  to  contrast  with  

■^  1000  1000 

of  one  solar  day,  as 


and  with  of  one  sidereal  day,  as 

1000 


51S4, 
is 
5169.846. 


The  difference  between  one  circular  day  of  5153000''''' and  one  sidereal 
day  of  5169846'^',  equals  4'  40''  46'''. 

Our  typical  form  is  diameter  6561,  circumference  20612.    Take  the  form: 

6.561  \       4      S.748 

rx-  = 

20.612)      3     27.48266666- 

where  27.4826666  is  taken  as  a  time  measure  of  the  moon  in  the  measure 

of  circular  days.     Reduce  to  solar  time,  thus: 

5153000 

27.482666+  X =  27.3183220164+  ; 

518^000 

or,  27d.  7h.  38'  23''  \'"  20"''. 

Add,  4'  40''  46''' 

the  above-stated  difference  between  a  circular  and  sidereal  day,  and  there 

results: 

27d.  7h.  43'  3^'  47'^'  20^'^^ 

or  the   exact   time  of   the  moon's  passage   around    the  earth.     (Parker's 

Quadrature,  page  116.) 


20  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 

Now,  above,  in  the  value  S7.48  inches,  we  find  we  have,  numerically,  the 
exact  diameter  to  the  base  of  this  time  value,  viz.,  2'j ./^S26-\- . 

It  seems,  considering  the  premises,  and  the  exactitude  of  the  results, 
tiiat  there  is  here  an  approximation  to  the    design  of  the  architect. 

{e.)  The  length  of  the  queen's  chamber  taken,  is 

226.21001  inches. 

Piazzi  Smythe  gives  this  length  measuring  the  north  side  of  the  room, 

at 

226.5  inches. 

But  says  he  judges  a  rough  probable  approximation  to  be 

226.  inches, 
giving  a  latitude  of  the  difference. 

\f.)  Just  as  we  see  that  the  upper  lines  seem  to  spring  from  conditions 
worked  out  by,  as  it  were,  anticipation  from  below  as  one  proceeds  up- 
ward, so  there  is  a  most  remarkable  showing  of  this  kind  with  relation 
to  this  taken  value  of  the  queen's  chamber  length  of 

226.21001  inches. 
Take  the  value  of  the  length  of  the  floor  line  of  the  ascending  passage- 
way, viz., 

123.68300698. 

In  inches  this  is  1484.19608376-I-. 

In  cubits  72.00640S1. 

1 4S4. 19608376+  inches  is  diameter  to  a  circumference  of 

4662.7419064  inches; 
or,  of,  in  cubits,  226.2149-)-  cubits; 

working  out  this  queen's  chamber  length,  in   inches  for  cubits,  to  within 

.005  of  an  inch. 
A  leading  idea  pervades  the  measures  used  in  this  chamber,  viz.,  that 
the}'  are  pure  circumference  values  connected  W4th  the  typical  form  20612. 
The  breadth  of  the  chamber  206.12  inches;  its  {east  and  west)  length  de- 
rived IVom  a  cubit  value;  the  uses  of  the  sidereal,  circular,  and  solar  day; 
and  so  on,  distinguish  it  thus.  This  is  in  contrast  with  the  measures  of 
the  king's  chamber,  which  are  as  follows: 

612  • 

(16.)  The  typical  form  is  20. inches  from  20612:  the  modi- 
fication is  20. ^ —,  a  diameter  value  (an  enlargement  on   i 

cubit).     On  this  last  form  all  the  measures  of  this  chamber  are 
founded. 


MEASURES    OF    INTERIOR    OF    GREAT    PYRAMID.  21 


.   2647   .       , 

{a.')  Breadth  206. inches; 

diameter  to  circumference  of  648  inches. 

15204-4-  . 
(/;.)   Length  =  breath  X  2=  412.-^! inches; 

diameter  to   circumference   of    1296    inches,   or    i    square  yard,   or 

the  y^  of  5184,  characteristic  of  the  solar  day. 

647001        192  1820  inches. 

(r.)  Height  2062. X =  229. 

1728 

T^-      •  o       1    ,  I  r    \  /:  28  inches. 

Piazzi  Smythe  s  measures  of  (a.)  •  200. 


{b.-)  412.5^ 


2 


Howard  Vyse's        "  (r.)  229. 

The  floor  Hne  of  the  king's  chamber,  or  the  line  k  a^  is,  verti- 
cally, by  Piazzi  Smythe,  7  inches  above  the  intersection  of  the 
floor  line  of  the  grand  gallery  with  the  vertical  axial  line  of  the 
mass. 

(17.)  The  length  of  the  line  k  d^  is  taken  at  330.  inches, 

differing  as   being   less  than   Piazzi   Smythe's  measure  by  .16248 
of  an  inch;  but  he  says  330.3^=  inches. 

330.13752  +  206.2647001   (=^'  a^)  ^  536.4019+  inches: 
for  which  see  Source  of  Measures,  page  138. 

Closing  these  specifications,  an  interesting  note  may  be  made 
of  the  variety  of  values  to  be  found  within  very  narrow  limits. 
By  this  system  of  measures,  taken  astronomically, 

^31415942.69+  X  2  =  62831885.38  equals  7926.^^-^ 
or  the  miles  equatorial   diameter  of  the  earth.      Now  take  the  line 
/^'  b^ :  it  is  in  length  13.61519648-}-  feet;  modify  this  by  the  addi- 
tion of  .00983206  of  a  foot,  making  it  13615 19648,  numerically. 

12  g  /- 

1361519648  X =  7926.-^ 


20612 

or  this  very  equatorial  value.     Such  results,   germane  to  the  sub- 
jects-matter of  the  general  construction,  serve  to  convince  one  of 


22  SUPPLEMENT    TO    SOURCE    OF  MEASURES. 


the  existence  of  permitted  extremes  on  a  mean  of  measures,  con- 
fined within  very  narrow  limits. 

It  is  seen  that,  from  first  to  last,  in  these  works  they  are 
founded  on  the  idea  of  co-ordination  of  measures  of  space  (in 
terms  of  the  British  measures)  with  those  of  time;  justifying  all 
that  the  author  advanced,  by  anticipation,  on  this  idea,  in  Source 
of  Measures. 

The  king's  chamber  dimensions  were  made  in  terms  for  com- 
puting tables  of  sines,  etc.,  though  not  immediately  apparent. 
The  Hindoos  have  the  same  method,  in  the  same  terms, 
coming  from  their  most  ancient  sources.  Thus,  in  computing 
the  sines,  they  take  the  radius  at  3437.74+.  (the  length  of  the 
king's  chamber  in  feet  being  34-3774+),  diameter  to  a  circum- 
ference of  10800,  which  circumference  multiplied  by  2  equals 
21600  7>iinutes ;  the  diameter  is  therefore  6875.48;  hence  the  pro- 
portion is — 

6875. 48-f  :   21600. 

Reduce  these  numbers  to  their  least  terms,  by  dividing  them  by 
36,  and  we  have — 

190.985+  :  600; 

where,  in  190.985,  we  have  10  times  the  height  of  the  king's 
chamber  in  feet.  (See  Bentley's  History  of  the  Hindoo  Astron- 
omy.) 


GEOMETRY 


23 


SECTION    III. 

Use  of  the  form  6561  :  20612  to  exhibit  values  of  changes  of 
geometrical  shapes  in  integral  numbers;  showing  numbers  to  be 
mental  creative  conceptions  to  which  shapes  are  obediences  as 
materializations:  also  other  geometrical  and  astrono7nical  uses 
of  this  form. 

PART  I. 


GEOMETRY. 

A  Circle  is  a  perfect  curve.  It  is  of  such  a  nature  that,  pro- 
tracted either  way,  it  will  re-enter  upon  itself.  The  length  value 
of  this  curve  being  found,  the  length  values  of  the  curve 
and  its  diameter  can  be  expressed  in  the  numerical  terms  of  this 
length. 

The  measure  of  circumference  of  all  regular  polygons,  includ- 
ing the  circle,  is  ^/^  the  circumference  by  the  radius  of  the  in- 
scribed circle.      (John  A.  Parker.) 

The  true  ratio  of  circumference  to  diameter  of  all  circles  is  4 
times  the  area  of  the  circle  inscribed  in  the  square  for  the  value 
of  circumference,  to  the  area  of  the  circumscribed  square  for  the 
value  of  diameter.      (Parker.) 

Given   diaineter  ^4  =  81,    area   oi  B  = 
6561,  area  of  y^  =  5153  'y  then, 
dia.  A 


X  cir.   of  A  ^  area   of  A 


or 


81 


X  circumference  of  A  =  5153 


81  X  cir.  of  A  =5153  X  4  =  20612 

20612 


circujnfercnce  of  A 


81 


24 


SUPPLEMENT     TO    SOURCE    OF    MEASURES. 


The  diameter  of  A  is  given,  and  therefore, 
diameter  :  circumference  :  :  8i  : 
and 


20612 


diameter  :  circumference  :  :  6561  :  20612 
(The  formulations  are  .those  of  Mr.  Charles  Home.) 
Thus  it  is  shown  that  the  area  of  the  square  of  81   to  the  side, 
or  6561,  being  taken  as  diameter  of  a  circle,  the  circumference  of 
that  circle  will  be  the  numerical  value  of  the  area  of  the  inscribed 
circle  multiplied  by  4,  or  5153  X  4  =  20612. 

The  number  forms  used  in  the  following  cases  are  6561  :  5153, 
and  6561  :  20612,  where  the  last  form  is  assumed  to  be  the  true, 
and  perfect,  and  only  integral  relation  of  diameter  to  circumfer- 
ence of  a  circle. 

Case  I. — Area  Measure. 


Side  of  B,  or  square,  equals  81.  Area 
of  B  equals  6561. 

Area  of  circle  A  equals  5153.  (John  A. 
Parker.) 


Case  II. — Linear  Measure. 


Diameter  of  A  equals  81^^6561  :  then 
circumference  of  A  equals  (Case  I.)  5153 
X  4  =  20612. 


But  since  the  above  are  but  measures  of  length,  one  would  sup- 
pose that  if  the  numerical  form  was  contained  in  nature,  as  a 
law,  it  should  exhibit  itself  as  integrally  applicable  to  solids. 
Therefore : 


GEOMETRY. 


25 


Case  III.  — Solid  Measure. 


H'xsa.  cube  of  81  to  the  edge;  A  is  its 
inscribed  sphere,  having  a  diameter  of 
8i. 


\ 

II 

\ 

A 

\ 

V 

__^^ 

\ 

\ 

The  usual  and  proper  formula  for  obtaining  the  solid  contents 

of  the  sphere  is 

— TT  diameter^. 
6 


We  have 
Then 


6561    :    20612    :  :    I    :   314159426914- 
X  81^  =  solidity  of  sphere. 


6561  X  6 
278262  =■  same. 

(This   result   is  the  same    as   3435u-  X  81,  and  34-351  ^^et  are 

T  2 

206. —    inches,    or    10    cubits,   and    are    the    breadth    (north   and 
south)  of  the  queen's  chamber.) 

278262  ^  20612  X  I3-5- 
Then  we  have — 
Solidity  of  cube  equals  8i^=  53i44i 

5 


Solidity  of  contained  sphere  equals 


20612  X  13- 


Case  IV. — Surface  Measure. 


Surface   of  cube  H  equals  area  of  one 
of  its  faces  multiplied  by  6,  or  81^  X  6  = 
39366 


\                     ^^ 

\ 

\ 

'^             A 

\ 

^ ^ 

\ 

26  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 

The    geometrical    formula    for   obtaining    the   surface   of    the 

sphere  is 

TT  diameter^. 
Then  we  have — 

X  6561  ^=^  surface  of  contain'ed  sphere. 


6561 
So  we  have — 
Surface  of  cube  of  81  to  the  edge  39366 

Surface  of  contained  sphere  20612 

Case     V.  —  Convex    surface    of    Cylinder,    of   height    and    diam- 
eter of  2)\,  coj7ipared  with  that  of  its  contained  Sphere. 

They  are  the  same,  viz : 
Surface  of  cylinder  20612 

Surface  of  sphere  20612 

Case  VI.  — Solidity  of  Cone,  Sphere  and  Cylinder. 

Where  the  altitudes  of  a  cylinder  and  of  a  cone,  and  the  diam- 
eters of  their  bases,  are  equal  to  the  diameter  of  a  sphere,  the  re- 
lation of  solidity  of  cone,  sphere,  and  cylinder  will  stand  as  i 
for  cone,  2  for  sphere,  and  3  for  cylinder,  as  was  proved  by  Ar- 
chimedes. 

Therefore,  the  solidity  of  the  sphere  of  a  diameter  of  81  being 

20612  X  13--=  278262, 
the  relative  measures  of  solidities  are  as  follows: 

Cone  with  altitude  and  diameter  o{  81  139131 

Sphere  with  diameter  oi  81  278262 

Cylinder  with  altitude  and  diameter  of  8i  417393 

Case  VII. — Integral  Numerical  Relations  between  the  Sphe7-e 
whose  diameter  {^side  of  Square,  and  diameter  and  height  of 
Cylinder^  is  81,  and  the  Convex  Surface  of  the  Cone,  the 
radius  of  whose  Base  is  81. 

If  the  height  of  the  cone  is  81,  the  slant  height  will  involve  a 
decimal  (in  the  diagonal  of  the  square  of  81).     We  therefore  have 


GEOMETRY. 


27 


to  resort  to  such  numbers  as  will  give  an  integral  value  for  the 
slant  height.  The  least  integral  values  applicable  to  the  measure 
of  a  right  angled  triangle  are  3  for  base,  4  for  height,  and  5  for 
hypotheneuse. 

As  a  cone  is  described  by  a  revo- 
lution of  the  right-angled  triangle 
about  its  perpendicular,  these  least 
integral  values  apply  to  the  elements 
of  the  cone.  A  B  \s  s,,  A  D  is  4, 
^  Z>  is  3,  and  the  base  of  the  cone 
is2  B  £>  =  6. 


(a.)  Multiply  these  last  numbers  by  27  : 

^  B  135 

A  D  108 

B  D  81 

{108    is  circumference  to  the  breadth   of   the   king's   chamber   in 

feet.) 

Solidity  of  sphere  (Case  III.)  is 

81'  X  ^;r  =  20612  X  135 

But  20612  is  circumference  to  a  diameter  of  Si'':  so  in  the  nu- 
merical elements  of  this  cone  there  is  a  correlation  with  the  solid- 
ity of  the  cube  of  81  and  its  contained  sphere,  as — 

Circumference  of  the  square  of  the  radius  of  base  multiplied  by 
Jjj  the  slant  height,  equals  the  solidity  of  the  sphere  contained 
in  the  cube  of  81  to  the  edge. 

(b.)   Y^  circwtiference  of  base  by  slant  height  equals  the  convex 
surface  of  the  cone. 
Then  the  convex  surface  of  this  cone  is  34353/^ 

(Breadth  of  queen's  chamber  equals  -^^'^^^^   =  17.1766+  feet.) 


28  SUPPLEMENT    TO  SOURCE    OF  MEASURES. 

(c.)  Multipy  these  values  by  8i,  and  we  have — 

A  B  10935 

A  D  8748 

BD  6561 

Convex  surface  is  ^  circumference  X  io935  =  22539220:  where 

the   radius    is    6561,    or   diameter  to   circumference   of    20612    (or 

5153  X  4),  and  the  height  is  6561  +  — —  ^  8748 

Here  we  have  this  correlating  relation  : 

•■•        /  7-  1     \         slant   height 

Circu77iference   of    radius    (as   a   diameter  value)  X — z — r^ 

•^  ^  81  X  10 

=  solidity  of  the  sphere  contained  in  the  cube  whose  edge  is  81. 

(Case  III.) 

{d.)  Multiply  the  values  in  ^rby  ij^,  and  we  have — 

A  B  14580 

AD  1 1664 

B  D  8748 

Here  are  elements  for  an   astronomical  application.  (Part  II. 
of  this  Section,  Case  III.) 

Aerain.      -^ ^   64800     is      circumference     to     diameter    of 

^  13-5 

20626.-^^^ —,   a  value  of  seconds  used  in  astronomy  to  obtain 

the  sun's  parallax  and  distance. 

Height    1 1664    is   dianuter  to    standard   circumference    of    great 

pyramid    in   inches.     This   diameter  as    11.- —    inches  was  taken 
by  the  Roman  nation  as  their  foot  measure. 

These  numerical  applications  teach  the  meaning  of  the  Egyp- 
tian symbol  of  a  man  standing  before  one  of  their  gods,  his  hand 
extended  supporting  on  its  palm  a  cone.  The  forearm  was  the 
cubit,  and  the  hand  was  the  palm,  or  a  division  of  the  cubit. 

Under  the  formula  for  solidity  of  a  cone,  viz : 

Yi  7z  R^  altitude. 

The  solidity  of  this  cone  is  by  equivalence — 


81-  X  81'  6561 


or  -^- —  X  8i 


3 


20612  20612 


GEOMPriRY. 


29 


Note.  A  numerical  source  of  almost  infinite  variations  of 
inter-connected  proportional  parts  on  these  forms  can  be  geo- 
nietrically  shown,  as  involving  at  once  values  peculiarly  the  prop- 
erty of  square,  circle,  triangle,  and  cone. 

K 


[     ^\^ 

//  ^^\^    ^\^ 

\\^\r^\ 

B 


D 


E 


A  Ft^2>,  a  H=g,  A  1=  27,  A  A'^  81. 

A  B  =  ^,  B  F=  5.  Let  A^  ^=40,  C  H=/^i,  A  D  =  t,6/^, 
D  I ^  365.     A  E=  3280,  E  K=  3281. 

Here  the- squares  are  multiples  of  the  number  3,  as  3,  9,  27,  81. 
The  triangles  are  of  a  nature  such  that  the  hypotheneuse  always 
exceeds  the  height  by  unity.  This  form  may  be  varied  from  in- 
finitely ;  and  as  to  methods  of  integral  triangulation,  see  Meyer's 
Quadrature  (Cincinnati.) 

The  square  of  81,  shown  herein  to  be  of  so  much  importance, 
is  founded  on  that  of  3,  which  is  the  base  of  a  triangle  from 
whence  such  curious  results  have  been  derived.  Take  a  use  of 
the  number  values  attached  to  these  triangles,  premising  that  the 
number  9  is  also  the  origin  of  the  sides  of  the  triangles,  as  4  -|-  5 
=  9,  9''  =  81  =  40  -f  41,  81  X  9  =^  729  =  365  +  364,  and  729  X  9 
=  6561  ^3281  -I-3280: 

Add  (i.)  365  X  2  ;;=  730.0000000004- 

(2.)  3280  32.800000000+- 

3280 


(3.) 


54 


.6074074074- 


Sum,  763.407407407 

And,  numerically,  we  have  the  standard  base   side   of  the  great 

pyramid  in  feet. 

But  763.4074074074-I-  X  54  =  20612 

which  use,  while  it  affords  data  the  same  as  in  all   the  cases  supra, 


30  SUPPLEMENT   TO   SOURCE    OF    MEASURES. 

also  shows  that  the  creative  conception  of  the  proportional  parts 
of  diameter  to  circumference  of  a  circle,  had  its  origin  in  that 
thought  symbolized  by  the  number  9 ;  so  that  diameter  is  not 
only  determinate  with  circumference,  but  they  are  merely  related 
issuances  from  the  common  source  of  9.  Another  use  of  this 
number  9,  producing  the  same  results  through  the  order  of  the 
digits,  might  be  given. 

Case  VIII.  —  Use  of  the  Diagonal  of  the  Square  of  Si. 

The  diagonal  of  the  square  of  81  is  a  mean  proportional  be- 
tween a  value  of  circumference  and  of  diameter  of  a  circle,  such 
that  one  extreme  is  diameter  to  circumference  of 

a  circle  of  360 ; 
which    value,    360,    for   circumference,   is  the  numerical  origin  of 
what  is  called — 

The  Analytical  Unit  of  Circular  Measure  ; 
where    the   angle    measuring  the   curve  of   a   circle,    shows   that 
curve  to  be  equal  in  length  to  the  radius. 

{a.)  We  have  the  form — 

47001-4- 
20612  :  6561  :  :  64800  :  20626—^ 

where  the  first  term  is  a  circumference  value,  and  the  last  is  a 
diameter  value    of  the   circle.     Divide   this  form  by   54,   and  we 

have 

.      6561 
381.7037037-f-  :  — —  :  :  1200  :  381.97166  + 
54 

where  the  first  term  is  the  standard  measure,  and  the  last  term  is 
the  exact  measure,  of  the  half  base  side  of  the  great  pyramid. 
(The    full    base    side,    then,    is   a   circumference  to   a  diameter,    as 

24  :  7.-^—,  where  24  can  be  taken  as  the  24  hours  into  which 

the   circle   of   360  is  divisible  by   15   parts  of  360  to  the  hour.) 

Multiply  this  last  form  by  -^-^,  and  we  have 

,      6561 
114.51111-I-  :  -^  :  :  360  :   114.5914999-!- 


GEOMETRY. 


31 


{b.)  The  diagonal  of  the  sjDhere  of  81  to  the  side  is — 

114.55129+ 
and,  as  a  fact,  this  is  a  mean  proportional  between  the  extremes 
in  the  last  form,  for  : 

114.5111+   :    114.5512+   ::    114.5512+:    114.5914+; 
which  shows  that  the   diagonal  of  this    square  of  81    has  a  pro- 
portional   connection    between   values  of  circumference  and  diam- 
eter of  the  circle  originating  from  the  number  9,  the  base  of  this 
square,  as  has  been  shown. 

(<:.)    But   the    extreme    114. 591499-]-   is 
diameter    to    a    circumference    of    360,    and 

the    radius    therefore    will    be   — —       ^; 

2 

57.2957499-}-.       Now,   where  a  portion  of 

the  arc  of  this  circle,  equal  in  length  to  the 

radius,  is  intercepted  between  the  radii,  the 

numerical  value   of  the    angle    measuring    this   arc   will    also  be 

equal  to  that  of  the  radius,   as 

radius=  57-295749  +  , 

intercepted  arc  =  same, 

contained  angle  =  same ; 

which  holds  true  of  no  other  values  assigned  whatever. 

The  angle  57°295-|-  is  that  one  which  will  always  give  the  in- 
tercepted arc  as  equal  to  the  radius,  but  any  other  value  given  to 
the  radius,  or  arc,  will  differ  numerically  from  the  value  of  the 
angle.  Hence  this  is  the  normal  numerical  value  giving  this 
geometrical  result. 

Hence,  circitmference  value  360  of  a  circle,  derived  from  the 
form  6561  :  20612,  which  is  taken  from  the  square  of  81  to  the 
side,  and  from  the  number  9,  becomes  the  normal  measuring 
circle  for  terrestrial  and  celestial  measures. 


32  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 


PART  II. 

Astronomical  use  of  the  form 
6561    :    20612 

Case  I. 

The  usual  measure  of  the  earth's  time  about  the  sun  has  been 
taken  in  the  terms  of  a  7iatural  measure  of  time,  viz.,  the  rising 
and  setting  of  the  sun.  By  long  continued  observation  the  nu- 
merical notation  of  this  period  of  time,  viz.,  the  solar  year,  has 
been  found  to  be,  in  the  terms  of  this  natural  measure, 

365. 256374-f- days. 

Now  suppose  that  while  this  is  so,  some  mental  creative  power 
had  thought  of,  and  willed  that  the  proportional  parts  of  the 
earth's  orbit,  as  regards  all  other  cosmical  measures,  should  cor- 
relate with  that  number  value  to  which  the  abstract  relation  of 
diameter  to  circumference  of  a  circle  is  found  to  render  obedience 
in  shape.  This  value,  as  thus  found  empirically,  can  be  relegated 
for  its  origin  to  circumference  values  of  a  circle,  taken  from  the 
form  6561   :   5153,  as  follows: 

360000000 

5153000 
103060 

31415 


365-256374+ 
where  360  is  the  normal  measuring  circle  derived  from  the  square 
of  81  and  the  form  6561  :  5153  (see  case  VIII.,  Part  I.),  5153  is  \ 
ci7xumfcrcnce  of  20612,  10306  is  \  circumference  of  20612, 
and  3 14 1 5  is  circumference  to  a  diameter  of  unity.  This  value 
of  the  year  can  not  be  reconstructed,  integrally,  from  a  common, 
or  unit,  numerical  source,  or  from  the  numerical  value  of  any 
shape  save  as  interpreted  by  the  above  form  of  6561  :  5153  only, 
and  alone. 


ASTRONOMY.  33 


Case  II.  — Diameters  of  the  Earth  in  Miles  from  the  form 

6561  :  20612 

((7.)  Take  circumference  derived  from  this  form  of  31415942.- 
6916162  :   Multiply  by  2,  and  we  have 

62831885.383324 
as  a  circumference  value.     Suppose  we  change  the  nature  of  this 
value  to  that  of  the   area   of  the   square.     Then  the  side  of  that 
square  will  equal 

^62831885.4-,  or  7926.^-^ 
which  in  miles  is  the  equatorial  diameter  of  the  earth. 

Here  is  a  change  of  numerical  notation,  comporting  with  a 
change  of  geometrical  shapes,  producing  this  result.  Consider 
how  we  have  found  in  the  pyramid  works  linear  measures  co- 
ordinating with  time  measures.  Here  we  find  the  same  thing 
with  the  addition  of  the  bringing  in  on  to  the  same  ground  the 
co-ordination  of  geometrical  shapes. 

ib.)  Reduce  this  miles  value  io  feet,  or 

7926.565X5280=  41852743.680 

Deduct  144135. 


Remainder,  41708608.680 


i 


which,  brought  back  to  miles,  gives 

■JC7-4- 
7899.''-^^^!-  miles; 

and  this  is  the  polar  diameter  of  the  earth  in  miles. 

Note.  This  value  144135  is  the  reverse  reading  oi  the  cube  of  81,  where 
8i3=  1531441.  It  is  a  biblical  use.  144  is  Adam,  and  135  is  A  S  H,  or 
xvo7nan,  and  it  is  stated  that  God  brought  the  woman  to  the  man  and 
joined  them,  or  144135,  which,  reversed,  is  the  cube  of  81.  Why,  for  in- 
stance, the  astronomical  formula  that  the  squares  of  the  times  are  as  the 
cubes  of  the  mean  distances,  is  so,  is  to  us  a  mystery.  It  simply  is  so  be- 
cause it  is  so:  it  is  part  of  the  faL  So  this,  to  us,  so  novel  use  of  reverse 
values,  if  found  to  be  useful,  or  used,  in  cosmical  developments,  must  be 
accepted  as  a  use  in  natural  building.  Here  it  seems  to  point  to  some 
method  of  notating  elliptical  properties. 


34  SUPP1.EMENT    TO    SOURCE    OF    MEASURES. 


/// 


Case  III.  —  The  Moon's   Time  from  Parker's  Quadrature. 

Mr.  Parker  takes  the  following  cosmic  values : 
The  solar  day  of  24  hours  has  5184000' 

The  sidereal  day  has  5169846' 

The  circular  day  has  5153000' 

where  this,  as  an  abstract  measure,  is  taken  as  the  ^  of  a  circum- 
ferejice  of  20612,   or  as   the  area  of  the  circle  in  the  square  of 

561. 

Take  the  form — 

20.612")       4      27.482666-}- 

\^-  = 
6.561)       3        8.748 

This   value    of    27.482666    as   circular  time,    reduced   to   solar 

time,  gives 

27.4826664- X  ^^  =  27.3183220164+ 

or  reduced  to  time  scale,  as  days,  gives 

27d.  7h.  38'  23"  1'"  2d'" 
To  this  add  the  difference  between  one  sidereal  and  one  cir- 
cular day,  or 

16846'"  =  4' 40"  46'" 
and  there  results 

27a.  7h.  43   3    47      20 
which  is  the  e.xact  value  of  the  moon's  period. 

Note.  By  Mr.  Parker,  the  time  of  a  sidereal  lunation  from 
the  best  authorities  when  he  wrote  was  2  7d.  7h.  43'  4"  against  his 
as  above,  showing  the  difference  of  i-  of  a  second.     The  solar  luna- 

tion  was  given  at  27d.  7h.  44'  3",  against  his  of  27d.  7h.  44'  2".— 

At  the  present  day,  this  value  of  the  solar  lunation  is  retained 

87 
as  27d.   7h.    44'   2".  — ,   agreeing  with   Parker  to  within  y^Q-  of  a 

second,  while,   however,   a  great  difference  has  been  made  as  to 

the  value  of  a  sidereal  lunation,  as  27d.    7h.  43'  ii"6t4;  for  this 

reason,  as  given  by  Godfray :   "This  is  the  value  at  present,  for 


ASTRONOMY.  35. 


r 


comparison  with  ancient  observations  led  Halley  to  the  conclu- 
sion that  the  moon's  mean  velocity  is  being  accelerated,  and  the 
period  of  a  revolution  shortened."  It  tells  badly  for  astronomi- 
cal accuracy  to  make  a  change  of  9"  in  such  a  period  on  the 
strength  of  ancient  records,  where  great  uncertainity  exists  as  to 
the  correct  chronological  periods  of  those  old  observations.  (See 
John  Von  Gumpach  on  Mr.  Airy,  the  Astronomer  Royal.) 

Case  IV. — Mean  Solar  Year  by  Air.  Parker 
He  takes  the  form 

206.12)        16      366.43555-1- 

65.61  )        9       116.64 
where  he  makes  366.4355-}-   the  base   for   the  calculation  of  the 
mean  solar  year.      By  simple  and  orderly  means  from  use  of  this 
form,  he  gives  this  value  at 

365d.  5h.  48'  50"  53'"  6"" 
His  steps  are : 
ist.      Circumference  value  as  stated  366.4355-}- 

2d.      Reduced  to  solar  time  by  the  factor  =^-  X 

5184 

3d.      He  adds  one  sidereal  day. 

4th.  He  adds  xy'i  of  the  excess  over  the  mean  between  one  cir- 
cular and  one  sidereal  day,  reduced  to  solar  time. 

Note.  There  is  a  method  of  use  of  the  form  of  113  :  355  for  obtaining 
the  year  value.  To  compare  and  force  the  form  113  :  355  by  that  of  6561: 
20612,  we  have 

6561  :  20612  :  :  113  :  355.000152415+ 
Then 

20612  :  20626.12 —  /'  c     1 
:  :  355-00015-415+  :  365-^56389+ 

54 

which  is   correct   as   compared  with    the   received  value   to   less  than   the 

16 


I 000000 


of  a  day  in  the  year's  period. 


36  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 

Case    V.  —  The   Angle  of  Solar  Paiallax,  and  the  Sun^s  mean 

distance. 

The  results  to  be  derived  from  the  late  transit  of  Venus  are  not 
expected  to  be  ranked  as  original  or  basic  data,  but  rather  as  data 
to  be  compared  with,  and  made  to  conform  to,  other  data  derived 
from  independent  sources.  A  very  high  authority  has  written  to 
this  effect,  and  gives  the  independent  results  as  follows : 

(i.)  By  the  effect  of  the  sun's  attraction  on  the  motion 
of  the  moon. 

Parallax  by  this  method,  8."  St* 

(2.)  By  measures  of  the  planet  Mars  when  nearest  the 
earth,  under  very  favorable  circumstances. 

Parallax  by  this  method,  8."  85 

(3.)  By  measuring  the  velocity  of  light. 

Parallax  by  this  method,  8."  86 

(4.)  By  an  independent  method  by  Leverrier. 

Parallax  by  this  method,  8."  83 

He  then  says  :  "From  the  general  accordance  of  these  various 
results,  it  would  appear  that  the  solar  parallax  must  lie  between 
pretty  narrow  limits,  probably  between  8"82  and  8"86."  Else- 
where, he  gives  the  result  as  8"84-|-. 

(a.)  The  astronomical  formula  for  obtaining  the  sun's  distance 

(see  Godfray's  Astronomy),  is 

TA-  ^  Radius  of  Earth 

Distance  of  sun  =  -— — — -. — 

o/«.    Horizon,    parallax 

and 

Radius  of  Earth 
Distance  =  Value  of  Sin.  Horizon,  parallax 

206264.7001 
(Here  206264.7001  is  assumed  as  the  correction  of  206264.8+  by 
Godfray.) 

(b.)  Now,  Mr.  Parker  has  also  a  form  for  finding  the  sun's 
distance  (see  his  Quadrature),  which  is 

distance  of  sun  =  diameter  of  earth  X  11664 


ASTRONOMY.  37 


where  11664  is  derived  from  his  original  form  as 

20612)         16        36643-555 

[  x-  = 
6561 3       9      1 1664 

He  takes  diameter  of  earth  as  mean  diameter,  for  which  he 
gives  no  sufficient  reason.  On  the  contrary,  the  author  takes  this 
as  the  equatorial  diameter  of  the  earth. 

(/:.)  Making  the  equations  in  (a.)  and  (d.)  equal, 

Radius  of  Earth 


Diameta  of  earth  X  11664=^^^^"^  ^^^-  ^^^^^-  Parallax 

206264.7001-}- 

which,  reduced,  gives. 

Value  j-z«.  horizontal  parallax  =  8.  "84193 

or  length  of  arc  8.84193; 

which  agrees  as  closely  as  seen  with  the  values  as  found  above, 

expected  to  be  confirmed  by  the  transit  observations.     It  must  be 

noted,  however,  that  the  transit  was  observed  the  earth  being  in 

perihelion,  and    therefore    this  result   of  8"84i93    being  taken  as 

the  mean,  the  results   of  the    transit  should  give  a  large  angle, 

say  8"9i,  or  thereabouts. 

{d.)  Taking  the  earth's  equatorial  diameter  as  found,  at  7926.656 
miles,  distance  of  sun  will  prove  to  be 

7926.656  X  1 1664  :=  92.456515  miles. 

(Note  here  the  use  of  this  value  20626.47001  in  this  parallax 
formula  and  in  the  pyramid  construction.) 

CasQ    VI. — General  Law  of  Interplanetaty  Distances. 

here  is  but  one  further  case  to  be  noticed  in  this  astronomical 
connection,  which  is  the  general  law  of  Kepler.     It  is  that 
The  squares  of  the  times  are  as   the  cubes  of  the  mean  distafices. 

This   terminology  fits  exactly  as  part  and  parcel  of,  and  as  a 
sequence  to,  the  method  herein  stated. 

So  we  have  in  these  sections : 

(i.)     A  Source  of  Measures;  Egyptian,   Roman,   British,  and, 
without  doubt,  Hebrew. 


38  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 


(2.)  The  great  pyramid  constructed  from  this  source;  essen- 
tially justifying  the  use  in  the  perfect  closing  of  the  lines  by  means 
of  its  rigid  application. 

(3.)  The  most  important  features  in  geometry  exhibiting  them- 
selves as  obediences  to  this  source,  as  to  a  creative  mandate. 

(4.)  And,  finally,  the  governing  features  of  astronomy,  as  to 
measures  of  space  and  time  relegating  themselves  to  this  same 
source,  as  to  a  creative  origin. 

Evidently  we  have  been  dealing  with  a  natural,  or  better  a 
Divine  system;  albeit  in  the  mist,  for  lack  of  a  right  method  of 
using  the  model  form. 


THE  LEGENDRE  AND  PLAYFAIR  METHOD.  39 


SECTION    IV. 

A  CRITICISM  ON  THE,  SO-CALLED,  LEGENDRE  AND  PLAYFAIR 
METHOD  OF  RECTIFICATION  OF  THE  CURVE  OF  THE  CIRCLE, 
BY  MEANS  OF  INSCRIBED  AND  CIRCUMSCRIBED  POLYGONS, 
SHOWING    ERROR    IN    THE    MEANS    EMPLOYED. 

§  I.  Where  an  erroneous  deduction  has  for  long  been  postulated 
and  accepted  as  a  truism,  the  error  of  such  a  deduction  must  be 
shown  as  a  first  step  toward  the  ascertainment  of  what  the  spe- 
cific truth  really  is. 

There  are  very  many  men  so  made  up  by  nature,  that  where 
by  long  habitude,  they  have  unconsciously  entertained  and  cher- 
ished a  postulate  which  perchance  is  radically  wrong,  they  pre- 
fer to  adhere,  as  by  custom,  to  the  error,  and  resolutely  close  their 
eyes  to  the  truth  ;  even  though  it  be  presented  to  them.  It  is  for 
this  reason,  chiefly  that  radical  reforms,  no  matter  in  what  de- 
partment of  culture,  are  so  obnoxious  to  a  conservatism  which, 
to  a  great  degree,  is  perhaps  as  necessary  to  the  well-being  of 
culture  as  truth  itself. 

But  sometimes  where  mighty  consequences  toward  the  better- 
ment of  humanity  offer  themselves  as  the  reward  of  the  estab- 
lishment of  a  primal  truth,  in  the  face  even  of  the  profoundest 
convictions,  entertained  and  cherished  for  never  so  long,  sup- 
ported even  by  the  highest  authorities  and  the  most  illustrious 
names,  the  hand  should  not  be  stayed  by  any  considerations  of 
conservatism,  from  pointing  out  radical  error. 

The  author  is  well  aware  of  the  obloquy  attaching  to  any  criti- 
cism of  the  kind  he  is  now  entering  upon ;  and  he  believes  he 
understands,  too,  that  really  this  kind  of  obloquy  is  shot  out  from 
a  very  base  interest  at  bottom,  which  desires  that  the  error  may 
prevail  rather  than  that  the  truth   may  be  ascertained.     He  ap- 


40 


SUPPLEMENT   TO    SOURCE    OF    MEASURES. 


peals,  therefore,  to  the  fair-minded,  to  give  this  criticism  a  care- 
ful reading  ;  he  being  perfectly  willing,  if  in  the  wrong,  to  bear 
the  jeers  usually  attendant  upon  any  effort  of  this  kind. 

§  2.  Before  proceeding  to  the  demonstration  of  error  in  the 
Legendre  or  Playfair  method  of  rectification  of  the  curve,  he  will 
give  two  instances  of  erroneous  deductions  connected  with  the 
subject-matter  of  apprdximate  values. 

{a.)  Sir  Isaac  Newton,  in  laying  the  foundations  of  his  Prin- 
cipia,  in  "Lemma  I.,"  postulates: 

"  Quantities  and  the  ratio  of  quantities  which,  in  any  finite  titne^ 
converge  continually  to  equality,  and,  before  that  time,  approach 
nearer,  the  one  to  the  other,  than  by  any  given  difference,  ulti- 
mately become  equal. '^ 

This  postulate  is  manifestly  untrue,  for :  let  ^4  ^  C  be  any  tri- 
angle, and  with  the  length  A  B  a.s  a.  radius,  let  the  arc  B  D  he 

drawn  to  intercept  the  line  A  C.  Sup- 
pose this  figure,  both  for  triangle  and 
segment  of  circle,  be  continually  and 
proportionately  reduced,  as  A  B'  C , 
A  B'  D' ;  the  relative  differences  wilt 
never  be  changed,  however  far  the  re- 
duction be  made,  and  consequently  the 
ratio  of  difference  will  always  remain 
the  same.  The  proposition  is  axiomatic, 
and  does  not  require  demonstration. 

But  take  the  triangle  ABC  with 
the  circular  area  A  B  D,  z.s  decreasing 
toward  A  B,  by  different  and  successive 
steps,  one  of  which  is,  say,  ABE,  with  the  circular  area 
A  B  F.  By  this  method,  no  geometrical  ratio  can  be  preserved. 
The  ratio  of  diminution  has  to  be  calculated  by  numerical  com- 
putations. But  there  being  a  ratio  of  diminution,  in  which  the 
difference  between  the  straight  line  and  the  curve,  is,  say,  a  de- 
creasing one,  it  is  nevertheless,  plainly  to  be  seen  that  the  only- 
equality  of  the  curved  line  B  D  with  the  straight  line  B  C,  in 


THE    LEGENDRE    AND    PLAYFAIR    MEl  HOD. 


41 


any  possible  diminution,  will  be  when  the  line  A  C  shall  so  close 
upon  A  B  as  to  wholly  coincide  with  it  (as  to  the  value  of  their 
lengths  now  or  at  last  becoming  alike),  and  become,  with  A  B, 
one  and  the  same  line,  at  which  stage,  or  condition,  there  can  be 
neither  curved  line  nor  straight  line  left  for  comparison  ;  ihere- 
fore,  so  long  as  these  lines — i.  e.,  C  B  straight,  and  B  D  curve — 
exist  at  all,  either  in  whole  or  in  part,  there  can,  by  possibility, 
be  no  equality  between  them. 

Hence,  the  '■'■Lemma"  is  false  in  its  terminology;  nor  is  it 
even  right  in  a  showing  of  a  growing  or  proximate  equality  of 
likeness  as  regards  the  ultimate  structure  of  these  different  kinds 
of  lines,  as  will  be  now  shown. 

(b?)  This  method  of  Legendre  and  Playfair  was  criticised  by 
Torelli,  as  thus  stated  by  Playfair  in  the  appendix  to  his  Euclid : 

"It  is  impossible,  from  the  relation  which  the  rectilineal  fig- 
ures inscribed  in,  and  circumscribed  about,  a  given  curve  have 
to  one  another,  to  conclude  anything  concerning  the  properties 
of  the  curvilineal  space  itself,  except  in  certain  circumstances 
which  he  has  not  mentioned." 

As  regards  this  statement,  Playfair  assumed  the  affirmative  as 
against  Torelli ;  and  yet,  as  to  the  structural  conditions,  or  prop- 
erties of  the  lines,  Torelli's  statement  can  be  demonstrated,  Play- 
fair to  the  contrary  notwithstanding.  This  is  to  be  seen  from  the 
following : 

The  burden  of  the  effort  of  Legen- 
dre and  Playfair  is  to  show  that,  by 
the  growing  diminution  and  equality 
between  the  circumscribed  C  B'  and 
the  inscribed  C  B,  the  curved  line 
penned  up  between  them  becomes 
measurable;  which  curved  line,  at 
any  stage  of  bisection,  being  an  even 
and  known  part  of  the  curve  of  the 
entire  circle,  from  it  the  length  of 
the  entire  circumference,  and  conse- 


42  SUPPLEMENT  TO  SOURCE  OF  MEASURES. 


quently  the  area  of  the  curved  space,  is  to  be  had.     The  measure 
of  this  growing  equality  is  always  to  be  tested'  by  the  difference, 
at  any  stage  of  bisection,  between   C  B  and  C  B' .     In  the  dia- 
gram,  which  may  stand   for  any  stage  of  bisection,    C  B'  is  the 
chord  of  half  the  arc,  and  therefore  E  E'  \s  B  B'  f6r  every  suc- 
ceeding bisection.     Now,   from   B'   as  a  center,  with    C  ^'  as  a 
radius,  describe  the  arc  C  D.     Then  C  D  will  be  the  quantity 
which  vanishing  by  diminution,   the  triangle   C  B'  C  will  event- 
ually, by  the  Lemma  of  Sir  Isaac  Newton,  become   C  B'  £>,  and 
isosceles;  when   the  curve  lying  between  C  B'  and  D  B'  must, 
by  hypothesis,  become  equal  to   C  B,  or  to  D  B',  as  a  straight 
line.     Such    being  the  conditions,    it  might   be  looked   for  as  a 
certainty   that   with   the  diminution   of    C   B,  an  accompanying 
diminution  would  take  place  in  E  E',  as  by  a  direct  ratio,  so  as 
to  exhibit  the  fact  of  growing  coalescence  of  the  curved  with  the 
straight  line.     But  to  the  contrary  of  this,   as  a   fact,   taking  the 
value  C  D  (the  difference  between   C  B  and  C  B')  and  E  E' 
for  a  number  of  bisections,  and  it  will  show  that,  with  relation  to 
the   diminution    of    C    D,  E   E'    is  ificrcasing.       It    becomes    a 
question,  on  the  showing,   whether  the  arc  is  not,   relatively,  sep- 
arating from,  instead  of  approaching  the  chord.      If  so,  the  ques- 
tion   is :  What  is  the  effect  of  this  ?     What  does  it  mean  ?     And 
this  question  is  left  to  the  reader  for  answer. 

Practically,  a  calculation  of  the  value  of  rr  to  6144  sides  of  the 
polygons,  taken  from  the  base  that  the  perimeter  of  the  polygon 
of  six  sides  is  one  with  25  cyphers,  making  the  radius  one  with  6 
repeated  24  times,  yields  the  following  data  as  to  the  relation,  or 
ratio,  between  C  D  and  E  E' ,  as  they  respectfully  diminish 
with  continuing  bisections  of  the  arc : 

6  sides,    C  D  :  E  E'  :  .   1   :  5.0706 

12      "  "  "  I   :  1.2404 

24      "  "  "  I   :  2.5301 

48     "  **  "  I   :  5-0847 

96      "  "  "  I   :        10.1818 


THE    LEGENDRE    AND    PLAYFAIR    METHOD. 


43 


192  sides, 

C  D 

£  E'   : 

:  I  : 

20.3697 

384  " 

( I 

(< 

I  : 

40.7426 

768  " 

<  I 

(f 

I  : 

81.4882 

1536  " 

(< 

(( 

I  : 

162.9917 

which  shows  a  rapid  ratio  of  diminution  of  C  D  with  relation 
to  that  oi  E  E'  \  and  the  practical  diminution  of  C  D  may  be 
judged  of  from  a  statement  of  its  value  at  6  sides  and  6144  sides, 
as  follows : 

6  sides,  C'  B'==  962250448649 

6sides,  C^'=  862730150341 


C  D,  or  difference,  99520298308 

6144  sides,  C  B'  000852211623 

6144  sides,  C  B'  00085221 1539 

C  Z>,  or  difference,  84 

which  simply  shows  that  the  triangle  C  B'  C  is  approaching  to 
being  isosceles  unattended  by  a  relatively  rapid  approximation,  in 
structure,  of  the  chord  C  B'  to  the  curve  C  B'.  But  the  rela- 
tion of  this  approximation  can  be  had  by  a  statement  of  the  con- 
tinuing ratios  between  B  B'  and  E  E',  and  these  are  as  follows: 


E  E'  for   6  sides 

B 

B'  :   :   X   : 

3-9318516 

12  " 

3.9828897 

24  " 

3.9989291 

48  " 

3.9997322 

96  - 

3-9999330 

192  " 

3.9999832 

384  " 

3.9999958 

768  " 

3.9999989 

1536  " 

((      |. 

:  3.9,999997 

-which  simply  shows  that  while  the  ratio  oi  E  E'  to  B  B'  can 
never  become  i  :  4,  the  ratio  of  C  D  X.o  E  E'  can  become 
I  :  Qo  large ;  or,  that  the  triangle  C  B'  C  may  become  isosce- 
les, while  yet,  absurdly  enough,  the  chord  and  arc  have  not  as 
yet  assimilated ;  not  only  so,  but  have  separated  by  a  relatively 
infinite  quantity. 


44 


SUPPLEMENT  TO   SOURCE    OF    MEASURES. 


These  instances  serve  to  qualify  the  estimation  now  had  of  the 
exactitude  of  the  foundation  conditions  in  this  speciaUty,  lying,  as 
they  do,  at  the  base  of  the  higher  regions  of  mathematical  science 
as  at  present  accepted ;  a  science  so  much  vaunted  as  being  ac- 
curate and  beyond  error.  They  serve  as  an  introduction  to  the 
following : 

§  3.  The  Legendre  or  Play  fair  method  of  obtaining  the  value 
of  TT,  or  rectification  of  the  curve  of  the  circle,  is  geometrically 
defective ;  and  is  insufficient  to  obtain  as  claimed  the  exact  nu- 
merical value  of  the  curve  to  within  less  than  any  assignable 
quantity. 

((7.)   The  Essential  Element  of  the  Playfair  Method. 

D  ^'       Let  C  D  B  be  the  ^  of  the  curve 

of  a  circle,  embraced  in  the  square 
polygon,  of  which  C  B'  is  the  side, 
and  itself  embracing  the  square 
polygon  of  which  C  P  is  the  side  : 
the  sides  of  these  polygons  being 
parallel  to  each  other  and  embraced, 
respectively,  between  the  radii  A  C 
and  A  B,  and  the  same  radii  ex- 
tended to  A  C  and  A  B' :  the  termini  of  the  side  C  B  oi  the 
inscribed  square  being  the  termini  C  and  B  of  the  embraced 
curved  C  D  B,  or  the  ^  part  of  the  circumference  of  the  circle, 
and  also  the  termini  C  and  B  of  the  radii  A  C  and  A  B.  The 
side  C  B'  of  the  circumscribed  square  touches  and  terminates  the 
radius  A  D  and  the  middle  of  the  curve  C  D  B,  in  the  point  D. 
The  reductions  of  the  sides  of  the  polygons  take  place  by  draw- 
ing the  chord  C  D  oi  the  curve,  or  arc,  C  D;  a.  perpendicular 
is  let  fall  from'^,  the  center  of  the  circle,  on  CD,  and  continued 
till  it  touches  the  curve,  necessarily  bisecting  the  curve  C  Z>, 
which  is  the  ^  part  of  the  entire  circumference.  C  D,  straight 
line,  is  the  side  of  the  second  inscribed  polygon.     The  radii  A  C 


THE    LEGENDRE    AND    PLAYFAIR    METHOD.  45 


and  A  D  are  extended  to  terminate  a  tangent  line  to  the  curve 
C  D,  drawn  parallel  to  C  D,  and  this  tangent  line  becomes  the 
side  of  the  second  circumscribed  polygon. 

This  process  is  continued  an  indefinite  number  of  times  agree- 
ably to  the  attainment  of  the  desired  exactitude  of  the  value  of 
the  curve.  The  value  of  the  curve,  as  regards  the  entire  circum- 
ference, is  always  known,  for  it  runs  down  with  succeeding  bi- 
sections from  \  to  |,  then  y^g-,  then  -^^,  and  so  on. 

Now  this  very  fact  (as  claimed),  viz.,  that  even  and  known 
portions,  as  \,  |,  jV'  sV'  ^"^  ^°  °"'  °^  ^^^  curve  of  the  entire  cir- 
cumference, are  respectively  limited,  ivholly  limited,  and  not  less 
than  limited,  between  the  sides  of  the  polygons,  as  bisections 
take  place,  is  that  on  which  the  method  of  Playfair  and  Legendre 
is  founded.  Thus,  it  is  absolutely  necessary  that  the  termini  C 
and  B  of  the  chord  C  B  shall  wholly  limit,  no  more  than  limit, 
and  exactly  terminate,  the  length  of  the  curve  C  D  B,  as  (in 
this  case)  \  part  of  the  circumference  of  the  circle.  The  same 
may  be  said  of  the  termini  C  and  D  of  the  chord  C  D,  of  half 
the  arc  C  D  B,  terminating  the  curve  C  D,  as  (in  this  case)  \  of 
the  circumference  of  the  circle ;  and  so  on  for  every  succeeding 
step  of  bisection.  And  this  fact  is  an  essential  element  in  this 
method. 

It  is  seen  that  the  geometrical  function  or  use  of  the  sides  of 
the  polygons  in  this  problem,  is  in  the  mere  mechanical  fact  of 
exactly  limiting  the  termini  of  the  curve  and  tiothing  more,  nothing 
less.  Apart  from  this  there  is  no  structural  relation  whatever 
between  the  right  lines  and  the  curved  line. 

It  so  happens  that  the  value  o{  A  C  and  C  E  being  known, 
we  have  J  A  C^  —  C  E''  =--  A  E ;  and  A  D  being  known,  A  D 
—  A  E=  D  E\  thus  we  have  the  value  of  the  sides  D  E  and 
C  ^  of  the  new  triangle  C  D  E,  oi  which  the  side  C  D  '\%  the 
chord  of  half  the  arc  C  D  B\  and  so  on.  Reduction  being  thus 
made  in  the  sides  of  the  polygons,  which,  as  claimed,  always  em- 
brace a  known  portion  of  the  curve  of  the   entire  circle,   when, 


46  SUPPLEMENT   TO   SOURCE   OF    MEASURES. 

at  some  remote  reduction,  the  sides  of  the  polygons  have  become 
exceedingly  small  in  value,  it  is  assumed  that  the  curved  line, 
penned  up  between  them  (a  known  portion  of  the  curve  of  the 
entire  circle),  is  of  the  same  value  with  that  of  the  reduced  sides 
of  the  polygons,  and  on  this  assumption,  which  is,  as  said,  de- 
pendent on  the  fact  of  the  exact  limitation  of  the  termini  of  the 
curve  by  the  termini  of  the  sides  of  the  polygons,  the  value  of 
the  circumference  of  the  circle  is  claimed  to  be  obtainable  to 
within  less  ihari  any  assignable  limit;  because  any  limit  being 
assigned,  the  bisections  can  be  continued  until  the  exactitude  of 
relation  shall  extend  to  and  beyond  the  assigned  limit. 

{b. )    The  Definitioji  of  a  Line. 

Modern  geometry  has  to  do,  and  only  to  do,  with  shapes  or 
magnitudes,  the  analysis  of  shapes,  and  the  relations  of  shapes, 
similar  or  dissimilar  to  each  other,  in  its  speciality.  If  number 
equivalents  are  used  in  modern  geometrical  analysis,  they  are 
simply  expressions  of,  and  translations  of,  geometrical  conditions 
into  another  and  an  equivalejit  form  of  expression.  The  defini- 
tion, arising  in  modern  geometry,  of  a  line,  that  it  has  length 
without  breadth  or  thickness  (as  numerically  a  i,  or  one,  of  length 
alone),  could  only  have  been  adopted  for  the  translation  of  geo- 
metrical conditions  into  other  forms  of  expression,  as  being  in 
the  fijst  place  permitted  by  geometrical  relations.  It  was  found 
that  admitting  breadth  of  a  line,  as  say  i,  or  one,  in  all  geomet- 
rical calculations  involving  the  use  of  right  lines,  the  value  of 
breadth  might  be  reduced  indefinitely,  and  finally  eliminated,  be- 
cause the  geometrical  discussions  of  plane  figures  admitted  of 
this.  It  was  assumption  to  unqualifiedly  make  use  of  the  same 
definition  as  regards  the  discussion  of  the  relation  between  right 
and  curved  lines,  in  calculations  of  the  sides  of  the  polygons,  as 
by  Legendre  and  Playfair,  without  first  showing  that  the  geomet- 
rical conditions  of  the  method,  as  it  progressed  in  the  bisections 
of  the  chords  of  the   arcs   by   means  of  the  calculations  of  the 


THE    LEGENDRE    AND    PLAYFAIR    METHOD.  47 

sides  of  the  polygons,  permitted  the  use  of  this  definition  as  ap- 
plying to  the  measure  of  the  curved  line  considered  to  be  penned 
up,  or  limited  between  the  sides  of  the  inscribed  and  circum- 
scribed polygons,  as  continued  and  successive  bisections  took 
place.  The  proper  and  very  first  step  in  the  problem^  as  it  is  one 
peculiar  to  itself,  and  occupying  a  place  sui  generis,  should  have 
been,  if  possible,  the  establishment  of  this  fact.  As  a  fact,  it 
seems  that  this  step  is  impossible. 

(c.)  Proof  of  the  correctness  of  the  definition  of  a  line,  that  it 
may  have  length  without  breadth  or  thickness,  when  applied 
to  the  admeasurement  of  plane  shapes,  or  magnitudes. 

The  propriety  of,  or  the  properness  of,  the  definition  of  a 
right  line  that  it  has  no  breadth,  or  thickness,  limiting  the  defi- 
nition to  the  discussion  of  plane  shapes,  can  be  exhibited  and 
proved  geometrically  ;  which  is  the  only  proper  mode  of  its  es- 
tablishment. 

Empirical  assumption  of  such  a  definition  would  be  but  geo- 
metrical quackery. 

In  the  right-angled  triangle  ABC, 
the  two  right  lines  B  C  D  D  and 
E  E'  F  F'  are  to  be  made  use  of 
as  half  sides  of  polygons  attempted  to 
be  embraced  between,  and  to  be  used 
to  measure  the  space  or  magnitude  be- 
tween the  bounds  A  C,  A  B,  and 
C  B,  and  E  E' ,  by,  if  possible,  a  re- 
duction of  the  lines  in  width,  they 
being  of  equal  breadth,  that  is,  B  D  ■= 

E  F.     These   lines   being   of   the    same   breadth,   /.    e.,    B  D  =^ 
E  F,  we  have  the  proportion 

A  E:  E  E'X  E  F  ::  A  B  ■  B  C  ^  B  D' ; 
where  E E'  X  F  F  and  B  C  Y^   B  D'  equal,   respectively,   the/ 
quadrangles,  or  lines,  E  E'  F  F\  and   B   C  D  I/.     But  since 


48 


SUPPLEMENT    TO    SOURCE  OF    MEASURES. 


E  F  =^  B  D,   dividing  the  second  and  fourth  terms  of  this  pro- 
portion oi  E  F  {=£  D),  we  have 

A  E:  E  £'  :  :  A  B  :  B  C ; 
where  E  E'  and  B  C  are  the  extreme  edges  of  these  lines,  ex- 
hibiting length  without  any  other  quality. 

{d.)  But  this  definition  is  not  good,  and  will  not  hold  good,  when 
attempted  to  be  applied  in  the  Flay/air  method  (a  special  one, 
and  siii  generis^,  to  the  admeasurement  of  the  curved  line  of 
the  circle. 

If  this  definition  is  to  be  applied  to  right  lines  as  measuring 
the  values  of  a  curved  line,  in  the  particular  problem  of  the  recti- 
fication of  the  curve  by  calculations  of  the  sides  of  the  inscribed 
and  circumscribed  polygons,  as  by  Playfair  and  Legendre,  then 
the  propriety,  or  properness,  of  this  definition,  as  thus  applied, 
should  be  susceptible  of  being  shown  also. 

Referring  now  to  the  fact  shown  in  {a.)  that  the  essential  fea- 
ture of  the  Playfair  problem,  or  method,  is  that  the  extremities, 
or  termini,  of  the  curved  line  claimed  to  be  penned  up  between 
the  sides  of  the  polygons,  are  wholly  defined,  wholly  limited,  ex- 
actly terminated,  no  more,  no  less,  by  the  ends  or  termini  of  the 
sides  of  the  polygons,  let  us  attempt  to  establish  Playfair's  and 
Legendre's  definition  of  a  line,  that  it  has  length  without  breadth, 
as  it  has  application,  and  as  they  do  apply  it,  to  the  admeasure- 
ment of  the  curved  line  of  the  circle,  embraced  between  the  sides 

of  the  polygons. 
,  ,       Testing    this    matter    and   leav- 

ing    out   of  view    that   right   line . 

■^   having     breadth     must    be    right- 


c'  angled  parallelograms,  as  A  B 
'^  B'  A',  and  C  D  D'  C ,  and  drop- 
ping consideration  of  the  sur- 
pluses of  these  lines,  viz.,  E  B  B' , 
and  F  D  D' ,  laying  outside  of 
the  area  O  B'  A :  Let  the  sides 
of    the      inscribed      and     circum- 


THE    LEGENDRE    AND    PLAYFAIR    METHOD.  49 

scribed  polygons  be  C  F  D'  C  and  A  E  B'  A',  limiting  between 
them  and  the  radius  0  A',  and  the  radius  O  D'  extended  to  B', 
the  curved  line  A  A'  D'  H,  which  has  the  same  breadth  A  A' 
(measured  on  the  radius  cutting  this  line,  viz.,  O  A')  with  the 
right  lines ;  that  '\<,,  C  C  =  A  A'  =  A  A',  for  the  breadth  of  the 
lines  straight  and  curved. 

It  is  seen  that  the  right  line  C  F  D  C  more  than  limits  the 
terminus,  or  end,  of  the  curved  line  jy  H,  by  the  excess  of  the 
value  of  the  area  C  F  H  H',  and  of  its  width  C  H' .  There- 
fore, as  the  gist  of  the  problem  by  Playfair  is  the  exactly  defining, 
the  wholly  limiting,  the  exactly  terminating,  no  more,  no  less,  of 
the  ends  of  the  curved  line,  by  the  ends  of  the  right  lines  \w  posi- 
tion (without  which  that  problem  is  a  geometrical  failure  for  ex- 
actitude), deduct  this  surplus  area  C  F  H  H'  (a  part  of  the 
right  line  C  F  D  C)  from  the  right  line  C  F  D'  C,  so  as  to 
leave  the  geometrical  condition  of  the  problem  as  exhibiting  that 
which  Legendre  and  Playfair  postulate  as  a  fact,  viz.,  that  the 
right  lines  always  (in  connection  with  the  radius  O  A'  and  the 
radius  O  D'  extended  to  O  B')  wholly  define,  wholly  limit,  ex- 
actly terminate,  no  more,  no  less,  the  termini  of  the  curved  line. 

This  being  done*,  which  is  an  essential  necessity  to  be  in  accord 
with  Legendre  and  Playfair,  the  right  lines  A  E  B'  A'  and 
C  D'  H  H'  remnant  oi  C  F  Lf  C  are  no  longer  in  a  condition, 
geometrically,  such  as  will  admit,  in  pari  passu,  of  their  reductions 
in  breadth  to  the  value  of  zero. 

In  {c.)  we  had 

A  E:  E  E'  X  E  F::  A  B  :  B  CX  B  n 
and  E  F  being  equal  to  B  D,  dividing  by  E  F,  we  have 

A  E:  E  E'  ::  A  B  :  B  C 
establishing  the  Playfair  definition  as  applicable  to  the  admeasure- 
ment of  plane  areas. 

But  here  O  C  :  C  D  X  H'  C  is  not  as  O  A'  :  A'  B'  X  A  A'. 
But  let  this  proportion  stand  as  true,  viz., 

O  C  :  C  D'  X  C  H'  ■  ■  O  A'  ■  A'  B  X  A  A; 
or  rather  as  taken  to  be  true  by  Playfair  and  Legendre,   for  they 


50  SUPPLEMENT   TO   SOURCE    OF    MEASURES. 


have  assumed  it  as  true,  though  A  A'  is  greater  than  C  H'  by  the 
value  C  H' .  Divide  this  proportion  by  the  value  A  A  to  obtain 
the  value  A  B'  as  a  line  without  any  other  quality  than  breadth. 
Diminishing  the  values  thus,  as  Playfair  does,  the  width  C  H' 
becomes  negative  as  to  value,  necessarily,  or  less  than  zero  in  its 
effect.  That  is,  the  lines  being  taken  at  zero,  as  to  breadth,  and 
taken  in  their  calculations  of  the  sides  of  the  polygons,  as  applying 
to  the  measure  of  the  curved  line  A  A  U  H  (reduced  in  its  breadth 
A  A,  in  pari  passu),  must,  necessarily,  as  a  practical  fact,  detract 
from  the  value  of  the  curve. 

Such  being  the  inevitable  fact,  resulting  from  assuming  the 
definition  of  a  line,  to  be  equally  applicable  in  this  particular 
and  especial  case,  wiih  its  use  as  applied  in  the  admeasurement 
of  plane  areas,  or  magnitudes,  Playfair's  method  is  defective  in 
the  geometrical  means  employed :  therefore  his  method  is  but 
proximately  right,  and  his  claim,  that,  by  his  method,  he  can  as- 
certain the  exact  value  of  the  curve  to  within  less  than  any  as- 
signable quantity,  is  false. 

As  a  resulting  truism,  the  value  of  the  curve  of  the  circle, 
as  worked  out  by  the  method  of  Playfair,  is  less  than  it  should  be. 

Q.  E.  D. 

Exeter,  December,  1875. 


NOTE  TO  PART  II. 


TESTS    FOR  correction  OF    THE  RESULT    BY  THE  PLAYFAIR   METHOD. 

(«.)  By  a  peculiar  method  of  test,  John  A.  Parker  shows  in 
his  Quadrature,  Proposition  III,  Appendix,  that  error  occurs  in 
the  sixth  decimal  place  of  the  Playfair  result. 

{b.)  Another  test  is  as  follows,  presuming  that  though  there  is 
inevitable  error  in  the  Playfair  method,  that  error  is  so  small  that 
it  is  to  be  found  in  a  far  off  decimal :  Take  a  disc  assumed  to  be 


THE    I.EGENDRE    AND    PLAYFAIR    METHOD.  51 

perfectly  circular,  the  greatest  distance  across  it  in  a  right  Hne 
must  be  integral  with  relation  to  its  bound  of  circumference,  be- 
cause the  lines  are  closed  with  relation  to  each  other.  Since  this 
is  so,  there  is,  and  must  be,  in  nature  an  integral  number  form 
which  will  exhibit  or  notate  this  perfect,  and  determined,  and  in- 
tegral relation.  Assuming  that  that  form  which  will  most  nearly 
restore  the  Playfair  result  is  one  that  will  correct  it,  then  the 
form 

113:355 
is  that  one  which,  divided  by  its  least  member,  gives 

I  :  3.1415929-I-; 

differing    from    the  Playfair   result  in   the  seventh  decimal  place. 

That  this  result  was  anciently   taken   as   corrective  of  this  same 

approximate  value,  its  presence  in  the  Bible  (as  the  first  face  one, 

underneath  which  the  Parker  form  of 

6561  :  20612 

lies  as  the  perfect  one),  sufficiently  shows. 

Besides  the  efforts  of  all  the  years  of  ancient  research,  modern 
efforts  have  failed  for  any  other  form  which  \v\\\  give  so  close  an 
approximate  to  the  Playfair  result  as  this  of  113  :  355.  The  ef- 
forts and  experience  of  ages,  therefore,  as  to  trial  for  this,  em- 
pirical though  they  be,  should  be  of  value  in  this  investigation, 
and  weight  of  authority  should  be  given  to  this  form. 

But  John  A.  Parker  rediscovered  the  form 

6561   :  5153  X  4=20612 

of  which  113  :  355  is  but  a  modification,  or,  from  which  it  is  but 

a  derivation  :  because 

,    ,  .  20611 

6561  :  20612  :  :  113  .  355 


20612  :  6561  :  :  355  :  113 


20612 

I 


>656i' 

while  testing  6561   :  20612   by    113  :  355,    integral  results  of  this 
peculiar  harmony  will  not  appear  in  both  proportions. 

On  the  ground  that  shapes  are  obediences  to  number  forms,  as 


52 


SUPPLEMENT   TO   SOURCE    OF    MEASURES. 


mental  creative  conceptions,  we  have  a  perfect  test  as  to  which 
of  these  forms  is  the  governing  one  in  the  proposition  that  the 
true  relation  of  circumference  to  diameter  is  4  times  the  area 
of  the  circle  inscribed  in  the  square  for  the  value  of  circumfer- 
ence to  the  area  of  the  containing  square  for  the  value  of  diam- 
eter, as  has  been  shown.  The  form  6561  for  area  of  square  to 
5153  for  area  of  inscribed  circle,  gives  under  this  rule  integration 
of  diameter  to  circumference  as  6561  :  5153  X  4  ^=  20612,  while 
no  such  result  attends  a  like  attempted  use  of  113  :  355.  (Par- 
ker's criticism.) 

These  considerations  ■(with  the  marvelous  results  as  to  the  use 
of  the  form  6561  :  20612  as  determining  geometrical  shapes  and 
astronomical  data  of  space  and  time  as  shown),  seem  to  have 
great  weight  in  determining  what  may  be  the  true  value  of  71,  and 
what  may  be  correction  of  the  manifest  error  in  the  Playfair 
method.  Attention  is  now  especially  directed  to  the  Quadrature 
of  the  Circle  by  John  A.  Parker  (John  Wiley  &  Son,  New 
York),  for  further  light  on  this  subject. 

The   following   formulations  are  given,    as   arising  from  use  of 
the  number  3^  =  9,   and  as    by  their  use   exhibiting   these  three 
noted  values  of  tt. 
20612 


54 


=  standard  ^  base  side  of  great  pyramid  := 

381.7037037037037 


(!•) 


381.7037037037037 


121. 5 


3141594269166+ 


the  Parker  value  of  n. 


(2.)  From 

381.7037037037037 

81  X  30 
deduct  ^  ■        ^      = 
Si'X  113 

Remainder, 

1638806948 

381.7035398230088 

381.7035398+ 
J21.5 

_355_ 
133 

3.1415929-+- 

or,  the  Metius  value  of  tc. 


THE    LEGENDRR    AND    PLAYFAIR    METHOD.  53 

(3.)  From  381-7037037037 

deduct,  2000000 


Remainder,  381.7035037037 

Add  37074 


Sum,  381.7035074111 

381.7035074111  ,,,^„,Ar,rR«n 

-~ =  3- 1415926535897 

or  the  accepted  value  of  tt  to  the  thirteenth  decimal  place. 


54  SUPPCEMENT    TO    SOURCE    OF    MEASURES. 


APPENDIX. 

An  illustration  may  be  seen  of  a  method  of  initi'al  steps  toward  the  re- 
sults involved  in  the  foregoing  treatise.  For  terminology,  let  the  cosmos 
be  considered  as  divided  into  the  technical  terms  heaven  and  earth.  Let 
earth  be  12,  and  heaven  be  12,  together  12  +  12  =24,  and  let  this  24  be 
divided  into  360  parts  of  15  parts  each.  Thus  we  have  the  terrestrial 
and  celestial  circle  of  360,  or  24  hours,  compassing  the  heavens  and  the 
earth. 

First  Genesis  says:  In  the  beginning  Elohim*  (God)  made  heaven 
(.y  m  i  m  =  12),  and  earth  (ar  tz  =  12). 

Then  the  text  says:  And  the  earth  (aretz)  was  T  H  V— V  B  H  V;  which 
words,  because  they  have  no  contextual  meaning,  Aben  Ezra  says  they 
must  simply  be  translated  idem  sonans,  as  T  H  V — V  B  H  V,  implying  an 
occultism;  (but  Dr.  Wordsworth  has  not  added  to  the  sublimity  of  the 
Scriptures,  by  translating  these  words  as  higgledy  piggledy). 

The  value  of  T  H  V  is  4,  5,  6,  and  gives  the  cone  from  the  triamrle  3,  4, 
5,  to  the  side  (page  27),  from  whence  all  the  pyramid  values  have  been 
seen  to  spring,  while  V"  B  H  V  is  6,  2,  5,  6,  or  6  X  -  X  5  X  ^  =  360,  which 
with  the  use  of  the  triangle  gives,  as  has  been  seen,  among  other  things, 
the  value  of  the  exact  solar  day.  Now  preparing  for  a  day  God  divided 
the  light  part  from  the  dark  part,  or  24  hours  or  parts,  into  specific  por- 
tions of  12  and  12,  the  natural  division;  then  He  divided,  so  the  text,  be- 
tiveen  the  light  and  between  the  dark,  or  a  cross  division  apparently  arbi- 
trary, but  perfecting  the  typical  square  of  4  in  one,  and  dividing  the  24  into 
4  equal  parts  of  6  each.  Darkness  was  taken  as  an  idea  implying  female, 
and  light  as  an  idea  implying  male.  So  the  day  was  divided  primarily  into 
a  male  portion  of  12  and  a  female  portion  of  12".     Six  (6)  days  finish  the 

*  Elohim  is  for  one  value  31415,  or  a  circumference  value,  designating 
the  origin  or  ground  method  of  circular  construction:  it  can  also  be  made 
to  signify  in  a  correlative  or  cognate  connection  401  X  3^  ^=  14436,  and 
144  X  36  =  51S4,  a  characteristic  of  an  origin  form  common  for  measures 
of  time  and  space,  for  5184  is  at  the  same  time  the  characteristic  of  a  solar 
day  in  thirds  and  of  the  square  yard  in  inches  muUiplied  by  4. 


APPENDIX.  55 


cosmos:    each    day   designated   as   an   evening  {ivotnan),  and  a  morning 

{man),  together  equaling  one  day-     So  there  are  in  the  6  days  a  total  of 

72  hours  ?K«/^  and  72  hours /<?;««/^,  in  all   144.     Tims  the  number   144  is 

born  by  use  of  12  and  12,  or  24;  and,  indeed,  12X1-=  i44- 

It  is  said  that  God  as  thus  finishing  the  6  days  of  the  cosmos,  made 

ADM  (the  word  used,  to  which  the  generic  term   man  is  here  wrongly 

given    by   translation,   nor  should    the   word  man  be  used  in  translation, 

until  the  close  of  the  garden  scene,  where  it  tirst  occurs);   but  this  word  is 

A  =  I,  D  =  4,  M  =-4,  or  144,  or  the  very  number  completing  the  6  days  of 

the  cosmos;  for  the  6  days,  as  seen,  have  together  made  144,  or  A   U   M. 

He  now  commands  them,  that   is,  the  male  and  female  parts  (so,  in  the 

text),  into  which   A  D  M  is  divided,  to  multiply,  and  as  correlatively,  or 

cognately,  the  144  has  been  divided  into  72  and  72,  then  72  X  7-  =51^4, 

which  equals  the  characteristic  of  the  solar  day  value  in  thirds,  just  where 

t;iS4 
it  co-ordinates  with  linear  measure,  for  ^— —  =  1296,  or  i   square  yard:  so 

that  thence,  as  a  common  source  (or  the  name  Jared,  or  Y  R  D,  or  En- 
glish yard),  there  may  be  a  weaving  together  of  time  and  distance  meas- 
ures as  inter-connecting,  and  inter-interpreting. 

Passing  over  the  7th  day  (as  empty,  or  nothing,  or  Hcbcl  [Abel],  or  a 
circle,  which  has  no  evening  nor  morning,  showing  a  unit  idea),  the  fore- 
going leads  up  to  the  construction  of  the  garden ;  for  it  says:  And  God 
planted  a  garden  in  Eden,  out  of  the  East.  Where  East  ?  East  from 
■where?  It  is  not  a  geographical  term,  because  it  referred  to  no  place  of 
departure.  The  word  is  M'  K  D  M,  and  is  4—144  (where  K  D  M  is  the 
equivalent  of  A  D  M  or  144).  So  God  planted  a  garden  in  Eden  com- 
posed of  4  squares  of  144  each.  Now  since  the  words  gn-odn.  ox  gar  den - 
Eden  equal  for  one  value  24  (or  ^  =  3  -(-«:=5-|-o=7  +  ''^='4  +  '*  =5 
:^  a  total  of  24),  and  since  A  D  M  is  a  square  area  of  144,  or  a  square  of 
12  for  length  of  side,  then  12  such  lengths  in  a  Irtgher  denomination  as  of 
feet  for  inches,  will  be  the  side  of  a  square  whose  area  is  144  square  feet 
(in  place  of  the  ADM  square  of  an  area  of  144  square  inches),  and  4  such 
squares  of  an  area,  each,  of  144  square  feet,  put  together  will  form  a 
square  of  2.\feet  to  the  side.  Then  these  squares  will  show,  first  an  area 
of  144  square  feet,  and  4  of  them  complete  the  garden,  truly  M'  K  D  M, 
or  4-144:  and  each  of  these  squares,  while  of  12  feet  to  the  side,  are  also 
144  inches  in  linear  measure,  for  12  X  i-  =  I44-  Thus  changing  the  A  D 
M  value  from  area  (144  square  inches)  to  linear  measure  (144  inches  in 
length),  we  have  an  interior  square  (central)  of  144  inches  to  the  side,  the 
nucleus  of  4  others  of  the  same  dimensions,  making  an  exterior  square  of 
288  inches  to  the  side  (or  24  feet),  or  a  total  circumference  of  288  X  4  = 


5^  SUPPLEMENT  TO  SOURCE  OF  MEASURES. 


1 152,  or  I  I  N  R  (or  place  these  letters  one. to  each  corner  of  a  square  and 
they  can  be  read  as  I  N  R  I).     So,  since  this  garden  is  seen  to  have  its 
origin  from  T44,  or  K  D  M  (or  A  DM,  for  this  last  is   144  also,  and  as  a 
fact,  the  two  words  A  D  M  and  K  D  M  give  us  the  name  Adam  Kadmon, 
whence  emanated  the  ten   Sephiroth  in  Hebrew  ,Kabbalism),  when  it  is 
said  that  God  placed  the  A  D  M,  or  144,  whom  he  had  made  in  this  gar- 
den, we  can  refer  this  placing  to  a  central  square  of  i  foot  to  the  side,  or 
of  an  area  of  144  square  inches.     Now  construct  a  pyramid  of  24  feet  to 
the  side,  and  nvhose  summit  shall  be  a  square  platform  of  i   foot  (or  144 
inches  area)  to  the  side:  multiply  these  values  by  100,  and  the  sides,  of 
the  base  and  summit,  will  be,  respectively,  2400  and   100  feet.     2400  feet 
is  circumference  to  a  diameter  of  763.9433+  feet,  the  actual  measure  of  the 
base  side  of  the  great  pyramid,  and  100  feet  will  be  a  circumference  to  a 
diameter  of  31.S309+  feet;  which  last,   allowing  for  the  finish,  or  pave- 
ment on  the  summit  of  the  great  pyramid,  now  removed,  may  be  assumed 
as  the  actual  measure  of  the  side  of  the  summit  platform  of  the  great  pyra- 
mid (see  Smythe's  measures  of  same;  roughly  made  about  400  inches  or 
ZZ-Vi  feet).     This  would  tend  to  show  that  the  pyramid  itself  was  in  its  fin- 
ished state  truncated  instead  of  being  carried  up  to  a  point.     And  this 
agrees  architecturally  with  Christian  kabbalism,  or  gnosticism,  for  Jesus,* 
or  I  H  S,  or  f  )7  f  ,  was  esteemed  the  corner  stone  finishing  a  structure  or 
dispensation,  and  the  gnostic  value  of  His  name  was,  for  one  value,  taken 
as  318,  or  the  numerical  value  of  diameter  to  a  circumference  of  unity 
[3.18+  is  diameter  to  a  circumference  of  10,  and  Abel  (Hebrew  H  B  L  = 
5  +  2  +  3  =  10 1,  who  is  (as  Adam  also)  a  prototype  of  Jesus,  is  in  value 
10,  so  that  the  I  H  S  value,  318,  notes  a  diameter  \.o  a  circumference  value 
of  Abel  or  10];  in  other  words,  He  was  with  the  Gnostics  the  cap-stone  of 
this  very  pyramid  of  the  garden,  and  of  Egypt,  as  finishing  it  with  a  cap, 
or  corner  stone,  the  base  of  which,  as  seen,  is  31. S+  feet,  or  diameter  to 
a  circumference  of  100.     Both  the  garden   and   gnostic  use,  and  their  es- 
sential inter-connection,  are  to  be  clearly  denoted  by  symbols,  which  once 
understood  can  never  be  dismissed  from  the  mind  as  part  and  parcel  of  the 
Biblical  scheme.     The  garden   as  a  square  of  12  -(-  12,  or  24  feet  to  the 
side,  or  28S  inches,  gives  a  circumference  of  the  square  of  2S8  X  4  ^  1152, 
as  designated  by  the   letters  I  =  i,  I  =  i,  N  =  5,  and  R  =  2;  which  letters, 

*  It  is  passing  strange,  but  while  Jesus  was  the  son  of  Joseph  the  car- 
f enter.  He  was  also  the  son  of  David:  now  DVD  (Hebrew  for  David) 
means  a  joiner,  thus  carpenter  and  joiner,  for  architectural  purposes, 
showing  a  building  system  in  the  very  construction  of  the  language,  in- 
dependently of  its  historical,  or  narrative,  use. 


APPENDIX. 


57 


placed  one  at  each  corner  of  the  square,  read  I  N  R  I  (and  1152-^-8  = 
A  D  M  or  144,  while  1215  -7-  5  =^  243  or  Abram).  Make  a  cube  of  this  gar- 
den of  24  to  the  side,  and  we  have  a  cube  of  S  cubes  of  12  feet  to  the  side 
each.  But  A  D  M,  or  Adam,  is  the  center  square  or  cube  of  12  inches, 
or  I  foot,  to  the  side,  and  therefore  he  is  concealed  in  the  very  heart  of  the 
cube,  thus: 


\ 

\ 

K 

i. 

N 

\^ 

\144  in. 

\ 

\ 

\  u,..\ 

288  in. 
24  tt. 


This  is  the  Jirsi  Adam;  as  placed  in  the  garden.  To  display  him,  or 
take  him  from  his  concealment,  unfold  this  cube  of  the  garden^  which,  by 
so  doing,  becomes,  in  display,  a  cross  with  the  man  Adam  exhibited  as 
a  square  (or  cube)  of  144,  as  seen. 


2''^  in. 


T7t. 


N 


24  ft. 


The  letters  I  I  N  R.  denoting  the  edge  measure  of  the  garden  multi- 
plied by  4,  to  give  circumference  of  the  larger  square,  or  24  feet  ^  2S8 
inches  X  4  =  1152,  are  found  located  one  at  each  corner  of  the  square 
of  24. 

The  Gnostics  denoted  this  the  second  Adam;  but  the  scheme  is  a  per- 
fect answer  to  the  Hebrew  scheme  of  the  first  Adam  in  the  garden. 

Now  since  the  ideas  as  to  the  cosmos  were  the  same  with  the  Hebrews 
as  with  the  Egyptians,  and  since  their  sacred  measures  were  the  same  (as 
is  provable  from  the  details  of  description  of  the  Temple  on  comparison 


58  SUPPLEMENT   TO    SOURCE    OF    MEASURES. 


with  the  pyramid  measures),  and  included  the  inch,  toot,  yard,  and  mile; 
and  since  all  the  structure?  of  the  Bibie,  as  the  Ark,  the  Tabernacle,  the 
Encampment,  and  the  Temple,  are  but  orderly  developments  from  a  BWa- 
shith  or  Beginning  (the  real  term  for  the  book  of  Genesis),  we  can  cer- 
tainl}'  look  upon  this  use  of  12^^  144  inches,  scaled  to  144  square  feet,  as 
the  simple  beginning  of  an  entire  sj'stem,  more  and  more  completely  de- 
veloped as  progress  is  made  in  the  books  of  the  Law;  and  then  made  use 
of  in  Temple  construction,  and  for  reference  to,  \)y  Ezekiel. 

The  similitude  between  the  Garden  of  Eden  and  the  pyramid  is  unmis- 
takable in  these  initial  steps;  which  once  taken,  a  great  variety  of  further 
steps  of  development  are  made  use  of,  all  pointing  to  the  primary  use  of 
the  forms  113  :  355  and  6561  :  20612.  For  instance:  ADM,  as  seen,  is 
taken  as  the  square  area  of  12  to  the  side.  After  the  woman  has  been 
created  in  this  prepared  garden,  Adam  says  of  her:  She  shall  be  called 
•woman  because  she  was  taken  out  of  mati.  Here  the  word  for  matt  is  not 
ADM,  but  A  I  S,  a  word  designative  of  something  from  whence  the 
■woman  could  be  produced.  This  new  word  reads  A  =  i,  I  =  i,  8^3,  or 
113,  or  diameter  to  355  as  a  circumference.'^  Use  113  as  a  square  area  as 
we  did  A  D  M,  then  the  side  of  its  square  will  be  •/113,  or  a  square  of 
10630+  to  the  side,  or  this  is  the  side  of  this  square  man.     The  woman 

was  taken  from  his  middle,  or  side,  or   loin,  and  —    gives  his  half,  or 

middle,  and  we  have,  by  the  division,  5315,  which,  in  Hebrew,  reads 
H'  A  S  H,  or  tJie  xvoman.  These  values  are  for  various  uses  in  determin- 
ing combinations:  among  them  place  these  figures,  one  to  each  corner  of 

a  square,  or 

I     5 

3  5 
and  we  can  read  5153,  which  is  the  area  of  the  circle  inscribed  in  the  square 
area  6561.  So,  also,  the  /"////values  of  the  letters  of  the  words  garden 
Edeti  or  gn-odn,  are  ^=3-j-«=50-f-o=:7o-(-(f  =  4-)-«-^50=a  total 
of  177.  Now  the  cubic  value  is  5.153  feet  divided  by  3  =  i. 71766  -(-  feet, 
10  cubits  are  17.1766+  feet.  The  surface  area  of  a  cube  of  10  cubits  to 
the  edge  is  1770+  feet;  so  that  the  garden  is  also  significant  of  a  reduced 
\alue  of  the  Jiolv  of  holies,  which  was  a  cube  of  10  cubits  to  t'he  edge;  as, 
also,  the  width  north  and  south    of  the  queen's   chamber   in  the  pyramid. 

*  In  modern  times  the  discoverer  of  this  quadrature  value  113  :  355,  is 
said  to  have  been  Peter  Metius;  but  this  seems  to  have  been  a  nom  ae 
guerre,  because  the  words  signify  the  measuring  stone. 


APPENDIX.  59 


Again,  the  number  9  is  prominentlj  suggested. 

While  A  D  M  is  144,  we  can  take  this  value  as  i  +  4  +  4  =^  9-  The  word 
A  S  H,  woman,  or  135,  can  similarly  be  taken  as  14-3  +  5:^9.  The 
serpent  is  the  letter  tcth,  or  a  serpent  coiled  with  its  tail  [spike  or. phallus) 
touching  the  opening  of  the  mouth  {yoni)  and  the  letter  tcth  stands  for 
the  number  9.  So  Adam,  and  the  -woman,  and  the  serpent,  are  one  in  the 
center  of  this  garden,  as  the  number  9.  Sharpe  says  the  hieroglyph  of 
the  letter  ^/;«e/ was  a  serpent  erecting  its  head  through  its  coils,  a  copu- 
lative symbol;  gimel  stands  for  the  number  3,  which,  inultipiied  by  itself, 
the  copulation,  will  produce  9,  which,  in  turn,  is  the  square  root  of  Si.  The 
tree  was  o-tz,  or  7  and  9,  as  to  which  7  is  a  female  number,  and  9  a  male 
number;  and  7X9  =  63,  or  reversed,  36.  36^=1296,  and  1296X4  = 
5184.     And  so  on. 

The  orderly  arrangement  from  B'rashith,  or  Beginning,  seems  a  de- 
scription, then  a  diagram,  as  of  the  garden;  then  an  explanation  and 
preparation  for  a  succeeding  diagram  in  the  ark  of  Noah,  where,  just  pre- 
ceding the  diagram,  the  full  and  even  detailed  measures  of  the  Egyptian 
pyramid  are  given.  (See  "Note"  at  close  of  Appendix.)  Then  follows 
a  preparation  for  a  further  development  under  Abram^  and  Lot,  and 
Sarah,  and  Isaac,  and  so  on,  closing  with  Jacob  and  his  sons  in  Egypt. 
Then  a  further  step  explained  in  diagram  by  the  Tabernacle  and  the  En- 
campment; and  so  on. 

Instance!  Abram  is  243,  the  J^  standard  height  of  the  pyramid,  taken  at 
243,  because  this  is  diameter  to  76 3. 4074074+,  which  in  feet  is  the  stand- 
ard length  of  t,he  base  side  of  the  pyramid.  Make  4  squares  of  243  to  the 
side  each,  with  4  inscribed  circles  of  a  circumference  of  763.-!-  each:  put 
these  4  squares  together,  and  we  have  a  large  square  of  486  to  the  side,  the 
standard  height  of  the  pyramid;  while  the  circumference  of  the  4  inscribed 
circles  give  the  total  length  {standard)  of  the  circumference  of  base 
.of  the  pyramid.  (The  name  Abraham  gives  further  detailed  measures,  as 
of  the  king's  chamber.)  To  get  the  exact  value  of  the  measures  of  the 
pyramid  we  had  the  change  from  20612  :  6561  to  64800  :  20626.47001 +. 
Now  the  name  Abram  giving  the  ground,  or  standard  form,  the  name  Lot 
gives  us  the  correlative  exact  form,  for  Abram  being  243,  the  yi  of  486,  Lot 
is  L  V  T  or  36  X  9  =  324,  and  324  is  the  %  of  648,  the  source  of  the  exact 
measures  of  the  pyramid  as  to  its  outside,  and  elsewhere,  in  contrast  with 
the  other  form  under  Abram.  (Both  values  are  brought  together,  when 
Moses  says:  Because  the  people  come  imto  tne  to  inquire  of  Elohitn; 
where  the  word  is  L'  D  R  S,  or  3-42-3,  showing  either  342  or  324.)  And 
so  on. 

The  Hebrew  word  I.uz.  the  foundation  of  so  much  kabbalistic  comment. 


6o  SUPPLEMENT    TO    SOURCE    OF    MEASURES. 


means  to  pervert,  to  say,  or  to  designate  one  thing  an  mean  another,  to 
invert  or  turn  end  for  end.  Its  value  is  3,  6,  7,  arid  inverted  it  is  763, 
showing  the  index  of  standard,  and  exact,  val.ue  of  base  side  of  the  pyra- 
mid. And  this  763  is  itself  a  perversion  for  2400,  because  it  implies  a 
diameter  to  a  circumference  of  2400.  The  word  is  taken  in  connection 
with  a  ^o«c  said  to  be  in  the  body  oi  man  (113),  or  Adam  (144),  which 
is  indestructible,  whence  new  life  must  always  spring.  Bone  is  a  form  of  the 
word  for  tree  in  the  garden,  for  one  is  otz,  and  the  other  otzm.  o-tz  is  7  X 
9  =  63,  or  inverted,  or  perverted,  36;  and  6336  is  the  mile  value  in  inches; 
while  otz-m  may  be  taken  as  36*  or  1296,  one  square  yard,  and  the  %  of  i 
solar  day  in  thirds,  or  as  36  X  4  =  ^44  or  Adam.  In  short,  the  use  of  these 
catchwords  refers  to  the  everlasting  duration  of  the  system  to  which  the}' 
are  mav  to  refer. 

L  V  Z  or  Luz  is  3,  6,  7:  Add  3  +  6  =  9,  then  from  L  V  Z  we  have  7,  9, 
=^otz  or  tree  in  the  garden;  append  final  metn,  or  square  ;«,  and  we  have 
otz-m,  or  bone;  showing  that  the  word  bone  is  thus  a  growth  from  Luz, 
involving  the  values  of  the  word  tree  in  the  garden. 

In  this  connection,  I  H  V  H  is  the  tetragrammaton ;  its  value  reads  from 
right  to  left  56501.  This  is  a  form  of  113  diameter  to  355,  for  113  X  5  = 
565,  and  this  can  be  placed  in  another  form  of  56.5  X  10,  meaning  this 
word.  But  to  show  another  use  take  the  same  form  as  being  multiplied 
irom  the  other  end,  or  1065  X  5  =  52S0  or  the  number  of  feet  in  a  mile. 

The  containment  by  the  Bible  of  this  system  is  in  no  manner  a  dispar- 
agement to  it  in  any  possible  point  of  view:  to  the  contrary,  if  this  sj'S- 
tem  of  exact  science  (call  it  so)  is  natural  and  divine,  then  indeed  the 
Bible  at  last  can  be  found  to  contain  those  exactitudes  of  Divine  work- 
manship which  can  not  be  interpreted  but  in  a  common  way:  therefore  a 
great  light  and  no  confusion  of  interpretation. 

A  language  thus  displayed  as  containing  a  number  system,  and  its  or- 
derly development  through  to  the  completion  of  a  most  perfect  unfolding 
of  the  cosmos  as  an  obedience  to,  or  materialization  of.  Divine  thought, 
brings  up  the  question  was  it  (or  is  it)  possible  for  men  to  so  construct  a 
language,  that  it  should  answer  all  the  ordinary  purposes  of  a  language, 
and  all  its  extraordinary  uses,  as  in  couching  the  most  wonderful  poetry 
of  the  world's  duration,  while  it  could,  in  harmonic  unison  with  historical 
use,  narrative  use,  familiar  social  use,  and  poetic  use,  blend  in  a  fully  de- 
veloped, numerical,  mathematical,  geometrical,  astronomical,  and  cosmi- 
cal  system  of  exact  enunciation  ?     Truly  it  bewilders  one. 

r 


APPENDIX.  6l 


NOTE  TO   APPENDIX. 

The  Adamic  chronology  ends  with  Lamech  and  Noah,  then  the  text 
proceeds  to  the  preparation  of  the  ark.  The  last  two  verses  [Gen.  v.  31, 
32)  seem  to  determine  the  measures  of  the  pyramid  in  another  but  an 
equivalent  set  of  measures  than  those  used  in  the  garden.  The  Hebrew 
reads  very  perculiarly  (besides  from  right  to  left),  in  such  form  that  a 
different  value  will  be  read  from  left  to  right.  It  says:  And  all  the  days 
of  Lamech  were  {sic  from  right  to  left) 

(years)  hundred  one  seven  and  (years)  seventy  and  seven. 
17  07  7 

Read  from  left  to  right,  the  cipher  becomes  meaningless,  and  the  values 
read. 

(i.)  1777- 

It  then  says:     And  Noah  was  Ben   Cfiomesk,  or 

son  of  5; 
that  is,  his  letters  are  N — ch,  or  5 — 8,  which  is  S  cubes  of  5  to  the  side, 
equals  a  cube  of  10  to  the  edge;  the  object  being  to  show  that  he  is  a  unit 
of  measure,  founded  on  the  number  5.  But  as  so7t  of  5  he  is  5,  which 
value  we  can  use  for  his  name,  as  we  can  the  number  3  in  place  of  the 
names  of  his  sons.  It  reads:  "  Noah  was  son  of  5,  one  hundred  (years), 
and  Noah  (5),  begat  eth  Shem,  eth  Cham,  and  eth  Japhet;"  that  is,  he  be- 
gat 3,  that  is,  Shem,  Ham,  and  Japhet.  So  reading  the  sentence  from 
right  to  left,  for  the  characteristic  numbers  denoted,  and  we  have 

3515 
which  arrangement  discovers 

(2.)  5153 

But  take  the  three  sons  as  mentioned,  and  we  have  (from  right  to  left) 

Shem,  M  S 

Ham,  M  Ch 

I 
and  Japhet,  T         P  V 

Substitute  the  values  of  the  letters,  in  the  same  order,  and  we  have 

(3-)  4  3 

4  8 

I 
4         S  6 


62  SUPPLEMENT   TO   SOURCE  OF    MEASURES. 


Again:  Noah  was  600  years  old.     He  was  the  son  of  Lamech;  and  the 
years  of  the  world  to  the  begetting  of  Noah,  were  1056 

Then  adding  the  600  of  Noah,  600 


Sum,  1656 

where  we  have,  by  reverse  reading, 
(4-)  6561 

Again:  1056  is  the  ^  of  one  mile,  for 

1056X5=^5280 
which  shadows  out  the  value 

10  5    6    5 
I  H  V  H 
or  the  yekovah  value  as  a  measure. 

In  (2.)  and  (4.)  we  have  6561:  5153  the  source  of  the  pyramid. 
In  (3.)  we  have  444,  381,  and  486,  and  in  (i.)  we  have  1777. 
Now  the  pyramid  in  circumference  of  base  is  1777  cubits;  in  length  of 
side  of  base  it  is  444  cubits;  and,  also,  in  length  of  side  of  base  it  is  381 
feet  multiplied  by  2;  and  its  height  is  4S6  feet. 

Thus,  in  development,  we  see  a  passage  from  the  use  of  the  number  12 
used  in  the  garden,  to  feet  and  cubits,  with  the  source  of  6561  :  5153;  be- 
sides, also,  the  other  form  of  113  ;  355,  which  is  contained  also  in  these 
verses,  but  more  obscurely. 


It  was  presented  to  the  inner  vision  of  Emanuel  Swer^enborg,  as  re- 
gards correspondences,  that  in  the  unseen,  as  here,  the  Hebrew  holds  the 
same  rank  as  a  language;  it  being  there  especially  the  vehicle  of  Divine 
teaching.  It  was  shown  him  as  to  its  uses,  that  it  is  understood,  or  read, 
agreeably  to  the  rank  of  the  heaven.  In  the  lowest  heaven  it  is  received  and 
appreciated  in  its  simple  narrative  form,  or  aspect;  while  he  says,  as  some- 
thing strange  to  his  understanding,  in  the  innermost  heaven  it  is  read  as 
consisting  of  numbers  which,  in  infinite  but  harmonic  arrangement,  teach 
the  Divine  constructive  process  of  the  entire  universe.  He  furthermore 
says,  that  it  is  there  the  love  and  delight  of  the  angelic  hosts  to  acquire 
from  the  contents  of  the  Divine  Book  fin  Hebrew),  as  numbers,  the  men- 
tal constructive  designs  of  the  Creator.  This  communication,  strange  to 
his  apprehension,  not  familiar  to  his  culture,  abrupth-  injected,  as  it  were, 
into  his  thought,  he  simply  enunciates  as  a  memorable  and  strange  teach- 
ing. The  instance  stands  out,  as  far  as  the  author  can  gather,  as  phe- 
nomenal in   all    Swedenborg's   writings,   as  a  matter  utterly  de    hers  his 


APPENDIX.  63 


natural  cognitions,  or  possible  conceptions.  Such,  being  the  case,  we,  to 
a  certain  extent,  find  that  however  he  came  by  the  enunciation,  he  was 
speaking  of  just  that  property  of  tne  language,  which  can  be  asserted  as, 
not  a  possibility,  but  its  discoverea  real  characteristic  m  the  Hebrew  Bible, 
in  the  uses  of  its  terms,  at  the  same  time  linguistic  and  numerical.  To  the 
author's  comprehension,  coupling  the  present  discovery  of  Biblical  use, 
with  Swedenborg's  assertion  made  over  one  hundred  j'ears  ago,  there 
arises  a  most  remarkable  test  of  the  spiritual  illumination  of  Swedenborg 
necessarily.  The  matter  grows  stranger  when,  in  these  present  discover- 
ies, very  learned  Jews  recognize  the  long  lost  keys  to  their  ancient  Kab- 
bala. 


Date  Due 


"W 


^^      JUL.  ^0  1330 


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